LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

Gl  FT    OF 

Class 


f 

DEPARTMENT  OF  THE  INTERIOR 

UNITED  STATES  GEOLOGICAL  SURVEY 

GEORGE  OTIS  SMITH,  DIRECTOR 


GEOGRAPHIC 


TABLES  AND  FORMULAS 


COMIM  I.KI>    BY 


SAMl'KL  S.  (JANNKTT 


WASHINGTON 

GOVERNMENT    PRINTING    OFFICE 

1908 


DEPARTMENT  OF  THE  INTERIOR 
UNITED  STATES  GEOLOGICAL  SURVEY 

GEORGE  OTIS  SMITH,  DIRECTOR 


GEOGRAPHIC 


TABLES  AND  FORMULAS 


COMPILED  BY 

SAMUEL  S.  GANNETT 


WASHINGTON 

GOVERNMENT    PRINTING     OFFICE 

1908 


r 

<fr 


CONTENTS. 


Rules  for  solution  of  right-angled  triangles 5 

Reduction  to  center 6 

Graphic  reduction  to  center 8 

Solution  of  triangles,  two  sides  and  included  angle  being  given 8 

Three-point  problem .- 9 

Graphic  solution  of  the  three-point  problem 11 

Micrometer  alidades — determination  of  constant  and  value  of  division 12 

Method  of  fixing  a  meridian  at  any  time  by  hour  angle 14 

Tables 16 

1.  Polaris:  times  of  culmination  and  elongation 16 

2.  Polaris:  azimuth  at  elongation 19 

3.  Polaris:  azimuths  at  different  hour  angles 20 

4.  Polaris:  azimuths  and  altitudes  at  different  hour  angles 26 

Example  of  use  of  projection  tables 35 

5.  Projections  for  large  areas 37 

6.  Projections:  scale  T^THF*  latitudes  0°  to  80° 49 

7.  Projections:  scale  ^^,  latitudes  0°  to  80° 59 

8.  Projections:  scale  ufas,  latitudes  25°  to  50° 71 

9.  Projections:  scale  ¥Tfonr,  latitudes  25°  to  50° 77 

10.  Projections:  scale  y^^,  latitudes  25°  to  50° 86 

11.  Areas  of  quadrilaterals;  1°  extent,  latitudes  0°  to  90° 95 

12.  Areas  of  quadrilaterals;  30'  extent,  latitudes  0°  to  90° 97 

13.  Areas  of  quadrilaterals;  157  extent,  latitudes  0°  to  90° 100 

14.  Areas  of  quadrilaterals;  10'  extent,  latitudes  0°  to  90° 106 

15.  For  conversion  of  arc  into  time Ill 

16.  For  conversion  of  time  into  arc 112 

17.  For  conversion  of  mean  time  into  sidereal  time 113 

18.  For  conversion  of  sidereal  time  into  mean  time ." 114 

19.  For  interconversion  of  feet  and  decimals  of  a  mile 115 

20.  For  conversion  of  wheel  revolutions  into  decimals  of  a  mile 116 

21.  Five-place  logarithms  of  natural  numbers 126 

22.  Five-place  logarithms  of  circular  functions  expressed  in  arc  and  time. .  148 

23.  Geodetic  position  computations 193 

24.  Log.  m,  for  use  in  computing  spherical  excess 271 

25.  Mean  refraction 272 

26.  Corrections  for  curvature  and  refraction 273 

27.  For  obtaining  differences  of  altitude 274 

28.  Horizontal  distances  and  elevations  from  stadia  readings 290 

29.  For  converting  metric  into  United  States  measures 299 

30.  For  converting  United  States  measures  into  metric 300 

31.  For  interconversion  of  miles  and  logarithms  of  meters 301 

Convenient  equivalents 313 

Constants 315 

Linear  expansion  of  metals 315 

Index 317 

3 

1  757J.2  - 


ILLUSTRATIONS. 


FIG.  1.  Solution  of  right-angled  triangles 5 

2.  Reduction  to  center 6 

3.  Solution  of  triangles;  two  sides  and  included  angle  given 8 

4.  Three-point  problem;  computation ; 10 

5.  Three-point  problem;  graphic  solution 11 

6.  Aspects  of  Polaris 14 

7.  Construction  of  polyconic  projection 35 

4 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


Compiled  by  S.  S.  GANNETT. 


RULES  FOR  SOLUTION  OF  RIGHT-ANGLED  TRIANGLES. 

The  "parts"  of  the  figures  are — 
H = hy  pothenuse, 
P= perpendicular, 
B=base, 
and  the  six  circular  functions  of  the  angle  a  at  the  base  of  the  triangle. 


FIG.  1. — Solution  of  right-angled  triangles. 

RULE  I.   The  product  of  two  opposite  parts  =  1,  .*.  either  is  the 
reciprocal  of  the  other. 

Example:  Tan  a  x  cot  a  —  1,  tan  <*—  of  a' 

Rule  II.  Each  part = adjacent  part  divided  by  the  following  part, 
.*.  each  part=the  product  of  the  adjacent  parts. 

cos  of  P 

Example:  Sin  a—       r>  sin  a—         B=HXcos  a. 


6 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


REDUCTION  TO  CENTER. 

In  fig.  2  let 

P= place  of  instrument; 
C= center  of  station; 

Q= measured  angle  at  P  between  two  objects,  A  and  B; 
y— angle  at  P  between  C  and  the  left-hand  object,  B; 
r= distance  CP; 

C'  =  unknown  and  required  angle  at  C; 
D= distance  AC; 

(r  and  D  must  be  reduced  to  same  unit,  usually  meters.) 
G=distance  BC; 
A = angle  at  A  between  P  and  C; 
B= angle  at  B  between  P  and  C. 


FIG.  2. — Reduction  to  center. 


Then,  from  the  relation  between  the  parts  of  the  triangle, 

G  :  r  ::  sin  y  :  sin  B; 
hence 

sin  B=^P- 

As  the  angles  at  A  and  B  are  very  small,  their  sines  may  be  regarded 
as  equal  to  A  sin  1"  and  B  sin  1",  respectively;  hence 

.  r  sin  y 
B=(m  seconds)Gsinl,, 

and 

sin  (Q=by)      r  sin  y 
D  sin  1"        G  sin  1"' 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


In  the  use  of  this  formula,  proper  attention  should  be  paid  to  the 
signs  of  sin  (Q+y)  and  sin  y\  for  the  first  term  will  be  positive  only 
when  (Q+y)  is  less  than  180°  (the  reverse  with  sin  y) ;  D  being  the 
distance  of  the  right-hand  object,  the  graduation  of  the  instrument 
running  from  left  to  right. 

r  being  relatively  small,  the  lengths  of  D  and  G  are  approximately 
computed  with  the  angle  Q. 

The  following  quantities  must  be  known  in  addition  to  the  measured 
angles  in  order  to  find  the  correction  for  reducing  to  center: 

1.  The  angle  measured  at  the  instrument,  P,  between  the  center  of 
the  signal  or  station,  C,  and  the  first-observed  station  to  the  right  of 
it,  A. 

2.  The  distance  from  the  center  of  the  instrument  to  the  center  of 
the  station  =  r. 

3.  The  approximate  distances,  D,  G,  etc.^  from  the  station  occupied 
to  the  stations  observed.     The  latter  may   be  computed  from  the 
uncorrected  angles. 

Example:  Reduction  to  center  from  P  to  C. 

Constants:  a.  c.  log  sin  1"  =5.  31443 

log  feet  to  log  meters  =9. 48402 

log  constant  (for  any  station)  4.  79845 

/•=6.5  feet:  log  =0.  81291 

log  constant  for  this  station  5.  61136 


Angle 
Q-Y 

(CPA) 
23°  40' 

Angle 

(BPC) 
37°14; 
or  322°  46' 

log  sin  angle 

9.  6036 

9.  7818 

a.  c.  log  distance  

5.  3954 

5.  3162 

log  T  -f-  constant 

5.6114 

5  6114 

log  correction  .              

0.  6104 

0.  7094 

correction  to  direction  

4".  08 

5".  12 

correction  to  angle  B  P  A=4".08  +5".12=9".20. 

GEOGRAPHIC   TABLES    AND    FORMULAS. 


GRAPHIC  REDUCTION  TO  CENTER. 

Approximate  closure  errors  of  triangles  may  be  tested  in  the  field 
before  distances  have  been  computed  by  scaling  from  the  plot  the 
distances  between  stations  in  miles  and  the  perpendicular  distance  in 
feet  from  signal  to  line  joining  instrument  and  distant  station. 

Then,  since  1  foot  at  a  distance  of  40  miles  subtends  an  angle  of  V 
(nearly), 

length  of  perpendicular  in  feet  X  40 

—  i—  —=  —  n  —  —  =  correction  in  seconds. 

number  ot  miles 

Example:  Station  P.  Correction  for  swing  on  line  B  P,  30  miles 
in  length  from  instrument  to  signal 

_3.8  feet  X  40  _ 

-^-         =  5  .1, 

correction  for  swing  on  line  A  P,  25  miles  in  length, 

2.6  feet  X  40 


and  correction  to  angle  B  P  A  =  Q  to  reduce  from  instrument  to  sig- 
nal =  5.1"  -f-  4.2"  =  9.3",  agreeing  closely  with  the  exact  compu- 
tation. 

APPROXIMATE    SPHERICAL    EXCESS    IN    SECONDS. 

This  may  be  obtained  by  dividing  the  area  of  the  triangle  in  square 
miles  by  75.5. 

SOLUTION    OF    TRIANGLES. 

Given  two  sides  and  included  angle,  to  solve  the  triangle: 


FIG.  3.— Solution  of  triangles;  two  sides  and  included  angle  given. 

Let  x  be  an  auxiliary  angle;  then 

tan  w—fr  or  log  tan  %=log  a— log  J; 

tan  i  (A-B)  =  tan  (a— 45°)  tan  ±  (A+B); 
i  (A+B)+*  (A-B)  =  A; 

i(A+B)-i(A-B)=B; 

from  which  remaining  parts  can  be  computed. 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


9 


Example: 


Gwen  log  a=4. 3666779       Given  C  (spherical  angle)  21°  14'  54".  10 
Given  log  6=4. 2050498       Given  |  sph.  exc.  -  .  10 


(1)  tan  *=0. 1616281 
«=55°  25'  25".41 

-45 

(5)  Logtan(z-43°)=10°25'  25".  41=9. 2647291 

(6)  Log  tan  79    22    33  .00=0.7268100 


C  (plane  angle)  =  21    14  54  .00  (2) 
180 

180°— C=A-(-B=158    45  06  .00  (3) 

i  (A+B)  =  79°  22'  33".  00  (4) 


9. 9915391=tan  i  (A-B) 


44    26    30  .90 


sum=A=123°  49'  03".  90  (8) 
difference=B=  34    56    02  .10  (9) 


(10) 


Check. 

A=123° 
B=  34 
C=  21 

49' 
56 
14 

03". 
02  . 
54  . 

90    a.  c. 
10 
00 

log  a 
log  sin 
log  sin 
log  sin 

=4.  3666779 
A=0.  0804971 
B=9.  7578749 
C=9.  5592012 

Sum  = 

180 

00 

00 

.00 

logc 
log  b 

=4. 
=4. 

0063762 
2050499 

THREE-POINT  PROBLEM. 

If  three  points,  forming  a  triangle  of  which  the  sides  and  angles  are 
known  or  can  be  computed,  be  visible  from  a  fourth  point,  P,  it  is 
required  to  determine  the  position  of  P. 

Set  up  the  theodolite  at  P  and  measure  the  two  angles  subtended  by 
any  two  of  the  given  sides. 

This  problem  is  of  use  in  cases  where,  the  regular  triangulation  hav- 
ing been  completed,  additional  points  are  required  for  the  topographic 
survey,  or  are  needed  for  special  service.  The  angles  should  be  care- 
fully measured,  and  in  the  computations  the  logarithms  should  be  car- 
ried to  seven  places  of  decimals. 

Three  cases  of  its  application  are  given,  as  in  others,  such  as  when 
P  falls  upon  one  or  another  of  the  sides  of  the  known  triangle,  or  on 
the  prolongation  of  either,  the  case  resolves  itself  into  the  solution  of 
a  simple  triangle  with  one  side  and  the  angles  given;  or  the  problem  is 
indeterminate,  as  when  P  is  situated  on  the  circumference  of  the  circle 
passing  through  the  three  known  points — a  contingency  which  rarely 
occurs. 


10 


GEOGRAPHIC   TABLES    AND    FORMULAS. 
Example  for  each  of  the  three  cases. 


Given  the  side      a=11204.5 
Given  the  side      6=  7289.0 
Given  the  side      c=  6273.8      x 
Given  the  angle  A =111°  10'  54" 


Angle  observed  A  P  C=P' 
Angle  observed  A  P  B=P" 
To  find  A  B  P=x 

To  find  A  C  P  =v 


FIG.  4. — Three-point  problem;  computation. 


P'...     50°  06'  12" 
P"..     43°  50'  38" 
S....  1800-i(A+P'+P") 
S....     77°  26'  08" 

c  sin  P' 


P' 49°  47'  20" 

P"..       .  44°  09'  30" 


S. 


KA-P'-P") 


S 8°  37'  02 


tan  Z= 


P'...  104°  00'  00" 
P"..  100°  20'  00" 

S  ____  180°—  £(A+P'+P" 
S  ____     22°  14'  33" 


tan  £=cot  (Z+45P)  tan  S 


b  sin  P" 

y = S  —  £,  but  if  tan  £  be  negative,  then  x  =  S  —  £,         y  =  S-{-s 


logc 3.7975307 

log  sin  P7 9.8849100 

colog  b 6.1373320 

colog  sin  P" 0. 1594574 

log  tan  Z 9.9792301 

Z...  43°  37X  49". 6 
logcot(Z-f45°)  8.3785397 
log  tan  S 0.6519386 


log  tan  £ . , 9.  0304783 

£ 6°  07X  21".7 

S...  .  77°  26'  08".0 


x.:..  83°  33'  29".7 

y 71°  18X  46".3 

Hence, 

P  AB 52°  35X  52".3 

P  AC..     .58°  35X  01".7 


Computation. 

logc 3.7975397 

log  sin  Px 9. 8839061 

colog  b 6.1373320 

colog  sin  P"....  0.1569894 


log  tan  Z 9.9747583 

Z...  43°  207  09".2 
logcot(Z+45°)  8.4631818 
log  tan  S 9.1805366 


log  tan  £ 7.6437184 


0°  15X  08".  1 
8°  37X  02".  0 


x 8°  52'  10".  1 

y 8°  21'  53".9 

Hence, 

P  A  B 126°  58'  19".9 

P  AC  ..  .  121°  50'  46".  1 


logc 3.7975307 

log  sin  P' 9. 9869041 

colog  6 6.1373320 

colog  sin  P" 0. 0071016 

log  tan  Z 9.9288684 

Z...  40°  19'  43".3 

log  cot  (Z+45°)  8.  9122794 

log  tan  S 9.6116787 


log  tan  £ 8. 5239581 

£...     1°  54'  50".04 
S...  22°  14'  33".00 


x...  24°  09'  23". 00 
y...  20°  19'  43".00 
Hence, 

PAB....  55°  30'  37".00 
PAC..  .  55°  40'  17".00 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


11 


As  all  the  angles  and  a  side  in  each  triangle  are  now  known,  the 
other  sides,  or  the  distances  from  P  to  the  three  given  points,  can  be 
readily  computed. 


TO 

PB 7194.87 

PA 8999.89 

PC 8107.98 

P  A  .  .  8999. 89 


PB 7194.94 

PA 1388.54 

PC 8107.91 

PA.,  .  1388.54 


P  B 5256.  29 

PA 2609.75 

PC 6203.63 

P  A  .  .  2609.  75 


The  results  are  verified  when  both  triangles  give  the  same  value  for 
the  line  P  A. 

GRAPHIC  SOLUTION  OF  THE  THREE-POINT  PROBLEM.  , 

1.  When   new  point  is  within  the  triangle  formed  by  the  three 
points,  point  sought  is  within  the  triangle  of  error. 

2.  When  new  point  is  on  or  near  the  circle  passing  through  the 
other  points,  the  location  is  uncertain. 

3.  When  new  point  is  within  either  of  the  three  shaded  segments  of 
the  circle  (see  diagram  below),  orient  on  middle  point;  then  the  line 
from  middle  point  lies  between  true  point  and  point  of  intersection 
of  lines  from  other  two  points. 

4.  When  new  point  is  without  the  circle,  orient  on  most  distant 
point;  then  the  point  sought  is  always  on  the  same  side  of  the  line 
from  most  distant  point  as  the  point  of  intersection  of  the  other  two 
lines. 

NOTE. — Since  a  location  can  be  made  from  any  three  points,  whether 
correctly  plotted  or  not,  therefore  always  check  such  locations  by 
means  of  a  fourth  point  if  possible. 


FIG.  5.— Three-point  problem;  graphic  solution. 


12 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


MICROMETER  ALIDADES— DETERMINATION  OF  CONSTANT 
AND  VALUE  OF  DIVISION. 

R',  R"  =  readings  of  micrometer  screw. 
R  =R'  —  R"  =  difference  of  readings. 

d  =  value  in  seconds  of  arc  of  1  division  of  micrometer  head. 

A  =  angle  subtended  by  targets  in  seconds  of  arc. 

C  =  micrometer  constant  or  ratio. 

H  =  distance  to  targets,  supposed  at  right  angles  to  line  of 

sight. 
B  =  length  of  base,  or  distance  between  targets. 


(D     d  = 
(2)     C 


B 


HR  sin.  I" 
1  HR 

B 


EXAMPLE. 


Readings  taken  on  two  targets  21.25  feet  apart  at  right  angles  to 
the  line  of  sight  and  at  a  measured  horizontal  distance  of  2859.5  feet 
from  the  point  of  observation. 

R'        R"         R 

550.0  -88.0  =  462.0 

540.5  -76.5  =  464.0 

etc.       etc.       etc. 

462.075  mean  of  20  readings. 


Computation  of  d  by  formula  (1) : 
B  =21.25  ft..  _  log.  1.32736 
H  =2859.5 ft..colog.  6.54371 

sin  1" colog.  5.31443 

R  =462.075  ft.  colog.  7.33528 


d=-3".317 log.  0.52078 


Computation  of  C  by  formula  (2) : 
B  =  21.25  ft.. colog.  8.67264 
H  =  2859.5 ft.. .log.  3.45629 
R  =462.075  ft.  Jog.  2.66472 

C  =62180..       ..log.  4.79365 


GEOGRAPHIC    TABLES    AND    FORMULAS.  13 

For  computing  distances  use  this  formula: 
(3)     H  =  ^ 

When  the  base  is  not  at  right  angles  to  the  line  of  sight  as  at  b,  or 
at  the  same  elevation  as  the  point  of  observation,  the  factors  sin  a 
and  cos  V  must  be  introduced,  a  being  the  angle  between  the  base 
and  line  of  sight  and  V  the  vertical  angle  at  A. 

The  full  formula  for  distances  then  becomes — 

(A\     TT      ^C  sin  a  cos  V 
R 

The  plotted  position  of  the  base  b  should  be  prolonged  on  the  field 
sheet  in  order  to  permit  the  measurement  of  the  angle  a  with  a  large 
paper  or  other  protractor,  with  greater  accuracy. 


14 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


METHOD  OF  FIXING  A  MERIDIAN  AT  ANY  TIME  BY  HOUR 


[Extracted  from  United  States  Land  Survey  Manual.] 

The  annexed  diagram  (fig.  6)  will  show  in  their  proper  relation  the 
various  aspects  of  Polaris  in  its  daily  apparent  motion  around  the 
north-polar  point. 

This  must  be  carefully  studied,  as  the  illustration  of  Table  1,  for 
finding  at  any  hour  the  hour  angle  and  azimuth  of  Polaris,  and  the 
resulting  meridian,  at  times  when  more  direct  methods  are  not  available. 

Hour  angle  of  Polaris.  —  In  fig.  6  the  full  vertical  line  represents  a 
portion  of  the  meridian  passing  through  the  zenith  Z  (the  point 
directly  overhead),  and  intersecting  the  northern  horizon  at  the  north 
point  N,  from  which,  for  surveying  purposes,  the  azimuths  of  Polaris 


FIG.  6.— Aspects  of  Polaris. 


are  reckoned  east  or  west.  The  meridian  is  pointed  out  by  the  plumb 
line  when  it  is  in  the  same  plane  with  the  eye  of  the  observer  and 
Polaris  on  the  meridian,  and  a  visual  representation  is  also  seen  in  the 
vertical  wire  of  the  transit,  when  it  covers  the  star  on  the  meridian. 
When  Polaris  crosses  the  meridian  it  is  said  to  culminate;  above  the 


GEOGRAPHIC    TABLES    AND    FORMULAS.  15 

pole  (at  S),  the  passage  is  called  the  upper  culmination,  in  contradis- 
tinction to  the  lower  culmination  (at  S'). 

In  the  diagram — which  the  surveyor  may  better  understand  by  hold- 
ing it  up  perpendicular  to  the  line  of  sight  when  he  looks  toward  the 
pole — Polaris  is  supposed  to  be  on  the  meridian,  where  it  will  be 
about  noon  on  April  10  of  each  year.  The  star  appears  to  revolve 
around  the  pole,  in  the  direction  of  the  arrows,  once  in  every  23h  56m.l 
of  mean  solar  time;  it  consequently  comes  to  and  crosses  the  meridian, 
or  culminates,  nearly  four  minutes  earlier  each  successive  day.  The 
apparent  motion  of  the  star  being  uniform,  one  quarter  of  the  circle 
will  (omitting  fractions)  be  described  in  5h  59m,  one  half  in  llh  58m,  and 
three  quarters  in  17h  57m.  For  the  positions  sn  S2,  S3,  etc.,  the  angles 
SPs1?  SPs2,  SPs3,  etc.,  are  called  hour  angles  of  Polaris,  for  the  instant 
the  star  is  at  s19  S2,  or  S3,  etc.,  and  they  are  measured  by  the  arcs  Ssn 
Ss2,  Ss3,  etc.,  expressed  (in  these  instructions)  in  mean  solar  (common 
clock)  time,  and  are  alwa}Ts  counted  from  the  upper  meridian  (at  S),  to 
the  west,  around  the  circle  from  Oh  Om  to  23h  56m.l,  and  may  have  any 
value  between  the  limits  named.  The  hoar  angles,  measured  by  the 
arcs  Ssn  Ss2,  Ss3,  Ss4,  Ss6,  and  Sstt,  are  approximately  lh  8m,  5h  55m, 
9h  4m,  14h  52m,  18h  Olm,  and  22h  48m,  respectively;  their  extent  is  also 
indicated  graphically  by  broken  fractional  circles  about  the  pole. 

Suppose  the  star  observed  at  the  point  S3;  the  time  it  was  at  S  (the 
time  of  upper  culmination),  taken  from  the  time  of  observation,  will 
leave  the  arc  Ss3,  or  the  hour  angle  at  the  instant  of  observation; 
similar  relations  will  obtain  when  the  star  is  observed  in  any  other 
position;  therefore,  in  general: 

Subtract  the  time  of  upper  culmination  from  the  correct  local  mean 
time  of  observation;  the  remainder  will  be  the  hour  angle  of  Polaris 
expressed  in  time,  w  the  " argument  for  Table  3." 

The  observation  may  be  made  at  any  instant  when  Polaris  is  visible, 
the  exact  time  being  carefully  noted. 


16 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLES. 

TABLE   1. — Local  mean  (astronomical}   time  of   the  culminations   and  elongations  of 

Polaris  in  the  year  1902. 

[From  Magnetic  Declination  Tables,  U.  S.  Coast  and  Geodetic  Survey.    Computed  for  latitude  40° 
north  and  longitude  90°  or  6h  west  of  Greenwich.]' 


Date. 

East  elonga- 
tion. 

Upper  culmi- 
nation. 

West  elonga- 
tion. 

Lower  culmi- 
nation. 

1902 
January  1  

h             m 

0     45.8 

h              m 

6    40.6 

h             m 

12     35.  3 

h              m 

18    38.  7 

January  15  

23    46.  6 

5     45.3 

11     40  0 

17    43  4 

February  1  

22     39.  5 

4    38.2 

10     32  9 

16    36  3 

February  15  

21     44.  2 

3    42.9 

9     37  7 

15     41  0 

March  1  

20    49.  0 

2    47.7 

8    42.4 

14    45  8 

March  15  

19    54.  0 

1     52.7 

7    47.3 

13    50.  7 

April  1  

18     47.  0 

0    45.6 

6    40.3 

12    43.  7 

April  15 

17    52  0 

23    46  7 

5     45  3 

11     48  6 

May  1 

16    49  1 

22    43  8 

4    42  5 

10    45  7 

May  15 

15    54.  2 

21     48  9 

3    47  6 

9    50  8 

June  1 

14    47.  5 

20    42.  3 

2    40  9 

8    44  2 

June  15 

13    52.  6 

19    47.  4 

1     46  0 

7    49  3 

July  1  

12    50.0 

18    44.8 

0    43.4 

6    46.7 

July  15 

11     55.  1 

17    49.  9 

23     44.  6 

5    51.8 

August  1 

10    48.  6 

16    43.  4 

22    38.  0 

4    45.3 

August  15 

9    53.7 

15    48.  5 

21     43.  1 

3    50.4 

September  1 

8    47.1 

14    41.  9 

20    36.  5 

2    43.8 

September  15    . 

7    52.  2 

13    47.  0 

19    41.  6 

1     48.9 

October  1  

6    49.3 

12    44.  1 

18    38.  7 

0    46.0 

October  15  

5    54.3 

11     49.  1 

17    43.  7 

23    47.  2 

November  1          

4    47.5 

10    42.3 

16    36.  9 

22    40.  4 

November  15            . 

3    52.3 

9     47.1 

15    41.8 

21     45.  2 

December  1          

2    49.3 

8    44.  1 

14     38.  8 

20    42.  2 

December  15.       

1    54.0 

7    48.8 

13     43.  6 

19    46.  9 

A.   To  refer  the  above  tabular  quantities  to  years  subsequent  to  1902: 

1.  4  minutes. 

up  to  March  1 


For  year  1903  add 
(add 


1904- 


2.8 


subtract  1. 1 


1905  add 

0.2 

1906  " 

1.5 

1907  " 

2.9 

1908  " 

J4.2 
[0.3 

1909  " 

L7 

1910  " 

3.0 

1911  " 

4.4 

on  and  after  March  1 


up  to  March  1 

on  and  after  March  1 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


17 


B.   To  refer  to  any  calendar  day  other  than  the  first  and  fifteenth  of 
each  month:  SUBTRACT  the  quantities  below  from  the  tabular  quantity 

for  the  PRECEDING  DATE. 


Day  of  month. 

Minutes. 

Number  of 
days 
elapsed. 

2  or  16 

3.9 

1 

3       17 

7.9 

2 

4       18 

11.8 

3 

5       19 

15.8 

4 

6       20 

19.7 

5 

7       21 

23.6 

6 

8       22 

27.6 

7 

9       23 

31.5 

8 

10       24 

35.5 

9 

11       25 

39.4 

10 

12       26 

43.3 

11 

13       27 

47.3 

12 

14       28 

51.2 

13 

29 

55.2 

14 

30 

59.1 

15 

31 

63.0 

16 

C.  To  refer  the  table  to  standard  time  and  to  the  civil  or  common 
method  of  reckoning: 

(a)  ADD  to  the  tabular  quantities  four  minutes  for  every  degree  of 
longitude  the  place  is  west  of  the  standard  meridian,  and  SUBTRACT 
when  the  place  is  east  of  the  standard  meridian. 

(6)  The  astronomical  day  begins  twelve  hours  after  the  civil  day,  i.  e. , 
begins  at  noon  on  the  civil  day  of  the  same  date,  and  is  reckoned  from 
0  to  24  hours.  Consequently  an  astronomical  time  less  than  twelve 
hours  refers  to  the  same  civil  day,  whereas  an  astronomical  time  greater 
than  twelve  hours  refers  to  the  morning  of  the  next  civil  day. 

It  will  be  noticed  that  for  the  tabular  year  two  eastern  elongations 
occur  on  January  12  and  two  western  elongations  on  July  12.  There 
are  also  two  upper  culminations  on  April  12  and  two  lower  culmina- 
tions on  October  12.  The  lower  culmination  either  follows  or  pre- 
cedes the  upper  culmination  by  llh  58m.l. 

D.  To  refer  to  any  other  than  the  tabular  latitude  between  the  limits 
of  25°  and  50°  north:  ADD  to  the  time  of  west  elongation  Om.13  for 
every  degree  south  of  40°,  and  SUBTRACT  from  the  time  of  west  elonga- 
tion Om.18  for  every  degree  north  of  40°.     Reverse  these  operations 
for  correcting  times  of  east  elongation. 

46061—08 2 


18  GEOGRAPHIC    TABLES    AND    FORMULAS. 

E.  To  refer  to  any  other  than  the  tabular  longitude:  ADD  Om.16  for 
each  15°  east  of  the  ninetieth  meridian,  and  SUBTRACT  Om.16  for  each 
15°  west  of  the  ninetieth  meridian. 

A  few  examples  will  illustrate  the  use  of  table  1. 

1.  Required  the  time  of  upper  culmination  of  Polaris  for  a  station  in  longitude  90° 
west,  for  March  3,  1904. 

h.        m. 

Astron.  time,  U.  C.  of  Polaris,  1904,  March  1 2    46.  6 

Reduction  for  two  days,  7m.9  (B)  (subtract) 7.9 

Local  mean  time  U.  C.  of  Polaris,  1904,  March  3 2    38.  7 

The  required  time  may  also  be  obtained  by  using  the  table  in  the 
opposite  direction,  i.  e.,  by  taking  the  time  for  March  15,  and  adding 
the  reduction  as  follows: 

h.      m. 

Astron.  time  U.  C.  of  Polaris,  1904,  March  15 1    51.  6 

Reduction  for  twelve  days,  add 47. 3 

Local  mean  time  U.  C.  of  Polaris,  1904,  March  3 2    38.  9 

In  this  case  the  two  results  are  practically  identical.  If  the  compu- 
tation is  made  both  ways,  the  results  will  check  each  other.  B  has 
been  inserted  to  save  the  surveyor  the  -little  trouble  of  making  the 
multiplications;  thus,  for  the  above  example,  in  the  table  under  B, 
opposite  the  third  or  seventeenth  day  of  the  month  in  the  left  hand 
column,  will  be  found  the  correction  7m.9. 

Computing  from  a  preceding  date,  for  days  between  April  11  and 
15  of  any  year,  the  reduction  in  B  will  be  greater  than  the  tabulated 
time  of  culmination,  in  which  case  23h  56m.l  will  be  added,  to  make 
the  subtraction  possible. 

2.  Required,  for  a  station  in  longitude  90°  west,  the  time  of  U.  C.  of  Polaris  for 

April  14,  1906: 

h.      m. 

Astron.  time,  U.  C.  of  Polaris,  1906,  April  1 0    47. 1 

Add..  23    56.1 


Sum 24    43.2 

Reduction  to  April  14,  subtract 51.  2 

Local  mean  time  U.  C.  of  Polaris,  April  14 23    52.  0 

Working  from  a  following  date,  for  days  between  9th  and  15th  of 

April,  the  sum  will  exceed  23h  56m.l,  and  when  this  occurs  subtract 

23h  56m.l  from  the  sum,  and  the  remainder  will  be  the  required  time. 

3.  Required,  for  a  station  in  longitude  90°  west,  the  time  of  U.  C.  of  Polaris  for 

April  10,  1904. 

h.        m. 

Astron.  time,  U.  C.  of  Polaris,  1904,  April  15 23    45.6 

Reduction  for  five  days,  add 19.  7 

Sum 24    05. 3 

Subtract..  ...     23    56.1 


Local  mean  time,  U.  C.  of  Polaris,  1904,  April  10 0    09. 2 

For  further  application  of  table  1  see  pp.  24  and  25. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  19 

TABLE  2. — Azimuth  of  Polaris  when  at  elongation  for  any  year  between  1902  and  1910. 


Latitude. 

1902.0 

1903.0 

1904.0 

1905.0 

1906.0 

1907.0 

1908.0 

1909.0 

1910.0 

O            ' 

o       / 

o       / 

o       / 

o       / 

o       / 

0            / 

0           / 

O           ' 

25° 

1  20.5 

1  20.1 

1  19.8 

1  19.4 

1  19.1 

1  18.7 

1  18.4 

1  18.1 

1  17.7 

26 

21.  L 

20.8 

20.5 

20.1 

19.8 

19.4 

19.1 

18.7 

18.4 

27 

21.9 

21.5 

21.2 

20.8 

20.5 

20.1 

19.8 

19.4 

19.1 

28 

22.6 

22.2 

21.9 

21.6 

21.3 

20.9 

20.5 

20.1 

19.8 

29 

23.4 

26.0 

22.7 

22.4 

22.1 

21.7 

21.3 

20.9 

20.5 

30 

24.2 

23.9 

23.5 

23.1 

22.8 

22.4 

22.1 

21.7 

21.3 

31 

26.1 

24.7 

24.4 

24.0 

23.6 

23.2 

22.9 

22.5 

22  2 

32 

26.0 

25.6 

25.3 

24.9 

24.5 

24.1 

23.8 

23.4 

23^1 

33 

27.0 

26.6 

26.2 

25.9 

25.5 

25.1 

24.7 

24.3 

24.0 

34 

28.0 

27.6 

27.2 

26.9 

26.5 

26.1 

25.7 

25.3 

25.0 

35 

29.0 

28.7 

28.3 

27.9 

27.5 

27.1 

26.8 

26.4 

26.0 

36 

30.1 

29.8 

29.4 

29.0 

28.6 

28.2 

27.9 

27.5 

27.1 

37 

31.3 

30.9 

30.5 

30.1 

29.7 

29.3 

29.0 

28.6 

28.2 

38 

32.6 

32.2 

31.8 

31.4 

31.0 

30.6 

30.2 

29.8 

29.4 

39 

33.9 

33.5 

33.1 

32.7 

32.3 

31.8 

31.4 

31.0 

30.6 

40 

35.2 

34.8 

34.4 

34.0 

33.6 

38.2 

32.8 

32.4 

32.0 

41 

36.7 

36.2 

35.8 

35.4 

35.0 

34.6 

34.2 

33.8 

33.4 

42 

38.2 

37.7 

37.3 

36.9 

36.5 

36.0 

35.6 

35.2 

34.8 

43 

39.8 

39.3 

38.9 

38.5 

38.1 

37.6 

37.2 

36.8 

36.3 

44 

41.4 

41.0 

40.5 

40.1 

39.7 

39.2 

38.8 

38.4 

37.9 

45 

43.2 

42.7 

42.3 

41.8 

41.4 

40.9 

40.5 

40.1 

39.6 

46 

45.0 

44.6 

44.2 

43.7 

43.2 

42.7 

42.3 

41.9 

41.4 

47 

46.9 

46.5 

46.0 

45.6 

45.1 

44.6 

44.2 

43.7 

43.3 

48 

49.0 

48.6 

48.1 

47.7 

47.2 

46.7 

46.3 

45.8 

45.3 

49 

51.2 

50.7 

50.2 

49.8 

49.3 

48.8 

48.4 

47.9 

47.4 

50 

1  53.5 

1  53.0 

1  52.5 

1  52.0 

1  51.5 

1  51.0 

1  50.6 

1  50.1 

1  49.6 

The  above  table  was  computed  with  mean  declination  of  Polaris  for 
each  year.  A  more  accurate  result  will  be  had  by  applying  to  the 
tabular  values  the  following  correction,  which  depends  on  the  difference 
of  the  mean  and  the  apparent  place  of  the  star.  The  deduced  azimuth 
will  in  general  be  correct  within  0'.3. 


For  middle  of— 

Correction. 

For  middle  of— 

Correction. 

January  

*  "••/ 

—0.4 

July  .  . 

/ 
+0.3 

February  

—0.3 

August 

-1-0  1 

March 

—0  2 

September 

0  1 

April 

0.0 

October 

0  3 

May  .. 

+0.2 

November 

—0  6 

June 

+0  3 

December 

0  g 

20 


GEOGRAPHIC   TABLES   AND   FORMULAS. 


TABLE  3. — Azimuths  of  Polaris 
[From  U.  S.  Land  Survey  Manual.    The  hour  angles  are  expressed  in  mean  solar  time.    The  occurrence 


STAB  AND  AZIMUTH. 

W.  of  N.  when  hour  angle  is  less  than  llh  58m. 
E.  of  N.  when  hour  angle  is  greater  than  llh  58m. 

POLARIS  above  THE  POLE. 

To  determine  the  true  meridian,  the  azi- 
muth will  be  laid  off  to  the  east  when  the 
hour  angle  is  less  than  llh  58m,  and  to  the 
west  when  greater  than  llh  58m. 

Time  argument,  the  star's  hour  angle  (or  23h  56m.l 
minus  the  star's  hour  angle),  for  the  year  — 

Hours. 

| 

i 

g 

! 

1 

j 

o 

«s 

1H 
rH 
OS 

Azimuths  for  latitude  — 

o 
30 

o 
32 

o 
34 

o 
36 

o 
38 

o 
40 

0 

42 

o 
44 

o 
46 

o 
48 

o 
50 

h. 
0 

m. 
0 
5 
9. 
14. 

19 

24 
28. 
33. 
38. 

43 

48 
53 

58 

m. 
0 
5 
9. 
14. 

19 
24 
29 
33. 
38. 

43. 
48 
53 

58 

m. 
0 
5 
9. 
14. 

19 

24 
29 
34 
38. 

43. 

48. 
53. 

58. 

m. 
0 
5 
9. 
14. 

19. 
24 
29 
34 
39 

44 

48. 
53. 

58. 

m. 
0 
5 
9. 
14. 

19. 
24. 
29 
34 
39 

44 
49 
54 
59 

m. 
0 
5 
10 
14. 

19. 
24. 
29. 
34. 
39 

44 

49 
54 
59 

TO. 

0 
5 
10 
14. 

19. 
24. 
29. 
34. 
39. 

44. 

49. 
54. 
59. 

m. 
0 
5 
10 
15 

19. 
24. 
29. 
34. 
39. 

44. 
49. 
54. 
IT 
5 

10 
15 
20. 
26 
31 

36. 

42 
47. 
53 

58. 

0 
2 
3. 
5. 

7 
9 
10. 
12. 
14 

16 
17. 
19. 
21. 
23 

25 
27 
28. 
30. 
32 

33. 
35. 
37 
39 
40. 

42. 
44 
46 
47. 
49. 

51 
53 

54. 
56. 

58 

0 
2 
3. 
5. 

7 
9 
11 
12. 
14. 

16 

18 
20 
21. 
23. 

25. 
27 
29 
31 
32. 

34. 
36 
38 
39. 
41. 

43 
45 

47 
40. 
50. 

52 
54 
56 
57. 
59. 

0 
2 
3. 
5. 

7. 
9 
11 
13 
14. 

16. 
18. 
20. 
22 
24 

26 
27. 
29. 
31. 
33 

35 

37 
38. 
40. 
42. 

44 

46 
48 
49. 
51. 

53. 
55. 

57 
59 

•eT 

63 
64. 
66. 
68. 
70 

72 
74 
76 
77. 
79. 

81. 
83 
85 
87 

0 
2 

0 
2 

0 
2 

0 
2 

0 
2 

0 

2 

0 
2. 

0 
2. 
5 

7 

9. 
12 
14. 
17 
19 

21. 
24 
26. 
29 
31. 

34 
36. 
39 
41. 
43. 

46 
48. 
50. 
53 
55 

57. 
— 
62. 
64. 
67 

69. 
72 
74. 
76. 
79 

81. 
84 
86 
88. 
91 

93. 
95. 
98 
100. 
103 

105 
107. 
110 
112 

5. 

7. 
9. 
11. 
13 
15 

17. 
19 
21 
22. 
24. 

26. 
28. 
30 
32 
34 

36 
38 
39. 
41. 
43. 

45. 
47 
49 
51 
53 

55 
56. 
58. 
— 
62. 

64. 
66 
68 
70 
72 

74 
75. 
77. 
79. 
81. 

83. 
85 
87 
89 

6 

8 
9. 
11. 
13. 
15. 

17. 
19. 
21. 
23. 
25 

27 
29 
31 
33 
35 

37 
39 
40. 
42. 
44. 

46. 
48. 
50. 
52. 
54. 

56. 

_58j 
"60 
62 
64 

66 
68 
70 
72 
74 

76 
77. 
79. 
81. 
83. 

85. 
87. 
89. 
91. 

6 

8 
10 
12 
14 
16 

18 
20 
22 
24 
26 

28 
30 
32 
34 
36 

38 
40 
42 
44 
46 

48 
60 
52 
54 
56 

58 

rio 

62 
64 
66 

68 
70 
72 
74 
76 

78 
80 
82 
84 
86 

&8 
90 
92 
94 

6 

8. 
10. 
12. 
14. 
16. 

18. 
20. 
22. 
25 
27 

29 
31 
33 
35 
37 

39. 
41. 
43. 

45. 
47. 

49. 
51. 
53. 

56 

^58_ 

60 
62 
64 
66 

68 

70 

72 
74. 
76. 
78. 

80. 
82. 
84. 
86. 
88. 

90. 
93 
95 
97 

6. 

8. 
10. 
13 
15 
17 

19. 
21. 

23. 
26 

28 

30 
32 
34. 
36. 
38. 

41 
43 
45 
47 
49 

51. 
53. 

55. 

57.| 
-60 

62 
64 
66 
68. 
70. 

72. 
74. 
77 
79 
81 

83 
85. 
87. 
89. 
91. 

94 
96 
98 
100 

6. 

9 
11 
13. 
15. 

18 

20 
22. 
24. 
27 
29 

31. 
33. 
36 
38 
40 

42. 
44. 
46. 
49 
51 

53. 

55. 
57. 
"60" 
62 

64. 
66. 
68. 
71 
73. 

75 

77. 
79. 
82 
84 

86 
88. 
90. 
92. 
95 

97 
99. 
101. 
103. 

7 

9 
11. 
14 
16 
18. 

21 
23 
25. 
28 
30 

32. 
35 
37. 
39. 
42 

44 
46. 
48. 
51 
53 

55. 
57. 
~ 
62 
64. 

66. 
69 
71. 
73. 
76 

78 
80. 

82. 
85 
87 

89. 
91. 
94 
96 
98. 

101 
103 
105. 
107. 

7. 
13 
18 
23 
28 

33. 
38. 
44 
49 
54. 

8 
13 
18 
23. 

28. 

33. 
39 
44. 
50 
55 

8. 
13. 
18. 
23. 
29 

34 

39. 
45 
50. 

55. 

8. 
14 
19 
24 
29. 

34. 
40 
45. 
51 

56. 

9 
14 
19. 
24. 
29. 

35 
40. 
46 
51. 
57 

9. 
14. 
19. 
25 
30 

35. 
41 

46. 
52 
57. 

9. 
15 
20 
25. 
30. 

36 
41. 
47 
52. 

58 

2 

0 
6 
11. 
17 
23 

29 
35 
41. 
48 
54. 

0. 
6. 
12 
18 
24 

30 
36 
42. 
49 
55. 

1. 

7 
12. 
18. 
24. 

30. 
37 
43. 
50 
56. 

2 
7. 
13. 
19. 
25. 

31. 
38 
44. 
51 

57. 

2. 
8. 
14 
20 
26 

32. 
38. 
45 
52 

58. 

3 
9 
15 
21 
27 

33 
39. 
46 
53 
59. 

4 
9. 
15. 
21. 

28 

34 
40. 
47 
54 

4. 
10. 
16. 

22. 

28. 

35 
41. 

48 
55 

1 

2 

9 
17 
25 
33 
42 

51 

PO- 

3 

1. 
8. 
16 
23. 
31. 

39. 

48. 

2. 
10 
17 
25 
33 

41 
50 
59. 

3. 
11 
18. 
26 
34. 

43 
52 

4. 
12 
19. 
27. 
35. 

44. 
53. 

6 
13 

21 
29 
37 

46 
55 

7 
14. 
22 
30. 
38. 

47. 
57 

8 
15. 
23. 
31. 
40. 

49. 
59 

60 
61. 
63. 
65 
67 

69 
70. 

72. 
74 
76 

77. 

61. 

63 
65 

66. 
68. 

70. 
72 
74 
76 

77. 

79. 

81. 
83 
85 

1. 
12. 
24 

37. 

53. 

3. 
14. 

26. 

40. 
57. 

5. 
16. 
29 

43. 

7. 
19 
32 

46. 

9. 
21 
34. 

50 

II 

23 
37 

53 

4 

8 
19. 

32 

46. 

10 
22 

34. 

50 

2 

6. 
42. 

11 

16 

79. 

5 

5 
40. 

10       16       23. 

32 

81 
83 

1 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


21 


for  the  use  of  surveyors. 

of  a  period  after  minutes  of  time  or  of  an  hour  angle  indicates  that  its  value  is  Om.5  greater  than  printed.] 


STAR  AND  AZIMUTH. 

W.  of  N.  when  hour  angle  is  less  than  11>>  58m. 
E.  of  N.  when  hour  angle  is  greater  than  llh  58™. 

POLARIS  below  THE  POLE, 

To  determine  the  true  meridian,  the  azi- 
muth will  be  laid  off  to  the  east  when  the 
hour  angle  is  less  than  llh  58m,  and  to  the 
west  when  greater  than  llh  58». 

Time  argument,  the  star's  hour  angle  (or23h  56m.l 
minus  the  star's  hour  angle),  for  the  year  — 

Hoars. 

I 

t 

t 

I 

1 

g 

0 

'  S 

— 

cs 

Azimuths  for  latitude— 

o 
30 

o 
32 

0 

34 

o 
36 

o 
38 

o 
40 

o 
42 

o 
44 

o 
46 

o 
48 

o 
50 

h. 
6 

m. 
9. 
45 

nt. 
40. 

in. 
34 
56. 

in. 
27 
52. 

m. 
18 

48. 

m. 
8 
44 

83 
81. 
79. 
78 

76 
74. 
72. 
71 
69 

67. 
65. 
64 
62 

60. 

85 

83 
81. 
79. 

77. 
76 
74 
72. 
70. 

68. 
67 
65 
63. 
6J. 

87 
85 
83 
81. 

79. 
77. 
76 
74 
72 

70. 
68. 
66. 
64. 
63 

61 

"isr 

57.' 
55. 
53. 

52 
50 
48 
46. 
44. 

42. 
40. 
39 
37 
35 

33. 
31. 
29. 

28 
26 

24 
22 
20. 
18. 
16. 

15 
13 
11 
9 

7. 

5. 
3. 
2 
0 

89 
87 
85 
83. 

81. 
79. 

77. 
76 

74 

72 

70 
48 
66. 
64. 

62. 
60. 

-5T 

57 
55 

53 
51 
49. 
47. 
45. 

43. 
41. 

40 
38 
36 

34 

32 
30. 

28. 
26. 

24. 
22. 
21 
19 
17 

15 
13. 
11. 
9. 

7. 

5. 
4 
2 
0 

91. 
89. 

87. 
85. 

83. 
81. 
79. 
77. 
75. 

74 
72 
70 
68 
66 

64 
62. 
60. 
58H 
56. 

54. 
52. 
50. 
48. 
46. 

44. 
43 
41 
39 
37 

35 
33 
31 
29 
27 

25. 
23 
21. 
19. 
17. 

15. 
13. 
11. 
9. 

8 

0 
4 
2 
0 

94 
92 
90 
88 

86 
84 
82 
80 

78 

76 
74 
72 
70 
68 

66 

64 
62 
|60 

Lir 

56 
54 
52 
50 

48 

46 

44 
42 
40 
38 

36 
34 
32 
30 

28 

26 
24 
22 
20 
18 

16 
14 
12 
10 
8 

6 
4 
2 
0 

97 
95 
93 
90. 

88. 
86. 
84. 
82. 
80. 

78. 
76. 
74. 
72 
70 

68 
66 
64 
62 
60 

100 
98 
96 

91. 

89. 
87. 
85. 
83 

81 
79 
77 
74. 
72. 

70. 
68 
66 
64 
62 

103. 
101. 
99. 
97 

95 
92. 
90. 

88. 
86 

84 
81. 
79. 
77. 
75 

73 
70. 
68. 
66 
64 

62 
59- 
57. 
55 
53 

50. 

48. 
46. 
44 
42 

39. 
37. 
35. 
33 
31 

28. 
26. 
24 
22 
20 

17. 
15. 
13 
11 
9 

6. 
4. 
2 
0 

107. 
105. 
103 
100. 

98. 
96 
94 
91. 
89 

87 

84. 
82. 
80 
78 

75. 
73 
71 
68. 
66. 

64 
|61. 
T5T 

57 
55 

52. 

50 
48 
45. 
43. 

41 
39 
36. 
34 
32 

29. 
27. 
25 
23 
20. 

18 
16 
13. 
11. 
9 

7 
4. 
2. 
0 

112 
109. 
107 
104. 

102 
100 
97. 
95 
92. 

90 

88 
85. 
83 
80. 

78 
76 
73. 
71 

68. 

66. 
64 
«. 

L5T 

57 

54. 

52 
49 
47. 
45 

42. 
40 
38 
35. 
33 

31 

28. 
26 
23. 
21. 

19 
16. 
14 
12 
9. 

7 
4. 
2. 
0 

m. 
39 

m. 
34 
57 

13 

27 
39. 
50. 

4 
18. 

31. 
42. 

53 

0. 

16 

29 
40. 
51. 

13 

26. 
38. 
49. 
59. 

10 

24 
36. 
47. 

57. 

7 

21. 
34. 
45. 
56 

4 

19 
32 
43. 
54 

0. 

16 
29. 
41. 
52. 

8 

2. 
11. 

20 
28 
36 
43. 
50. 

57. 

1 
10 

18. 
27 
35 
42. 
49. 

56. 

8. 

17. 
25. 
33. 
41. 
48. 

55. 

7 

16 
24. 
32. 
40 
47. 

54. 

5. 

14. 
23 
31 
39 
46. 

53. 

4 

13 
21. 
30 

38 
45. 

52. 

2. 

11. 
20. 
28. 
36. 
44. 

51. 

59 

1 

10 
19 
27. 
35. 
43 

50. 

58 

58. 
57 
55 
53. 
51. 

49. 
48 
46 
44. 
42. 

41 

39 
37. 
35. 
34 

32 
30 

28. 
26. 
25 

23 
21. 
19. 

18 
16 

14 
12. 
10. 
9 

7 

5. 
3. 
2 
0 

59. 
58 
56 
54. 
52. 

50. 
49 
47 
45. 
43. 

41. 
40 
38 
36 
34. 

32. 
31 
29 
27 
25. 

23. 
22 
20 
18 
16. 

14. 
12. 
11 
9 

7 

5. 
3. 
2 
0 

» 

4. 
11 
17. 
24 

30 
36 
42 
48 
54 

59. 

3. 
10. 
17 
23 

29. 
35. 
41. 
47. 
53 

59 

2. 
9. 
16 
22. 

28. 
35 
41 
47 
52. 

58. 

1. 
8. 
15 
21. 

28 
34 
40 
46 
52 

57. 

1 
7. 
14. 
20. 

27 
33. 
39. 
45. 
51. 

57 

c 

6. 
13. 
20 

26. 
32. 
38. 
45 
51 

56. 

5. 
12 
19 

25. 
32 
•38 
44 
50 

56 

5 

»  n- 

18 

24. 
31 
37. 
43. 
49. 

55. 

58 
55. 
53. 
51. 
49. 

47. 
45. 
43. 
41 
39 

37 
35 
33 
31 
29 

27 
25 
22. 
20. 

18. 

16. 
14. 
12. 
10. 

8 

6 
4 
2 
0 

59. 
57. 
55. 
53. 
51 

49 
47 
45 
42. 
40. 

38. 
36 
34 
32 
30 

27. 
25. 
23. 
21. 
19 

17 
15 

12. 
10. 

8. 

6. 
4 
2 

0 

To 

5 
10. 
16 
21. 

27 
32 
37. 
42. 
48 

53 

58 

1. 
10 
15. 
21 

26. 
32 
37 
42. 
47. 

52. 

58 

4 
9. 
15 
20. 

26 
31. 
36. 
42 
47. 

52. 

57. 

3. 
9 
14. 
20 

25. 
31 
36. 
41. 

47 

52 

57. 

3 
8. 
14 
19. 

25 
30. 
36- 
41. 
46. 

52 
57 

2. 
8 
13. 
19. 

25 
30 
35. 
41 
46. 

51. 

57 

2 
7. 
13 
19 

24. 
30 
35 
40. 
46 

51 
56. 

1. 
7 
12. 

18. 

24 
29. 
35 
40 
45. 

51 

56 

11 

3 
8. 
13. 

18. 
23. 
28. 
33. 
38. 

43. 

48 
53 
58 

3 
8 
13 

18 
23 
28. 
33 
38 

43 

48 
53 
58 

2. 
8 
13 

18 
23 
28 
33 
38 

43 

48 
53 

58 

2. 
7. 
12. 

18 
23 
28 
33 
38 

43 

48 
53 
58 

2 
7 
12. 

17. 
22. 
28 
33 
38 

43 
48 
53 

58 

2 
7 
12. 

17. 
22. 
27. 
33 
38 

43 

48 
53 
58 

1. 
7 
12 

17. 
22. 
27. 
32. 
38 

43 

48 
53 
58 

1. 
6. 
12 

17 
22 
27. 
32. 
37. 

43 
48 
53 

58 

22  GEOGRAPHIC  TABLES  AND  FORMULAS. 

Table  3  gives  for  various  hour  angles,  expressed  in  mean  solar  time 
and  for  even  degrees  of  latitude  from  30  to  50  degrees,  the  azimuths 
of  Polaris  for  eight  years,  computed  for  average  values  of  the  north 
polar  distance  of  the  star,  the  arguments  being  the  hour  angle  (or  23h 
56m.l  minus  the  hour  angle  when  the  latter  exceeds  llh  58m),  which 
is  termed  the  time  argument, a  and  the  latitude  of  the  place  of  obser- 
vation. The  table  is  so  extended  that  azimuths  may  be  taken  out  by 
inspection  and  all  interpolation  avoided,  except  such  as  can  be  per- 
formed mentally. 

The  hours  of  the  "time  arguments  "  are  placed  in  the  columns  headed 
"  hours,"  on  the  left  of  each  page.  The  minutes  of  the  time  argu- 
ments will  be  found  in  the  columns  marked  um,"  under  the  years  for 
which  they  are  computed,  and  they  are  included  between  the  same 
heavy  zigzag  lines  which  inclose  the  hours  to  which  they  belong. 

The  time  arguments  are  given  to  the  nearest  half  minute;  the  occur- 
rence of  a  period  after  the  minutes  of  any  one  of  them  indicates  that 
its  value  is  Om.5  greater  than  printed,  the  table  being  so  arranged 
to  economize  space. 

The  table  will  be  used  as  follows:  Find  the  hours  of  the  time  argu- 
ment in  the  left-hand  column  of  either  page;  then,  between  the  heavy 
lines  which  inclose  the  hours,  find  the  minutes  in  the  column  marked 
at  the  top  with  the  current  year.  On  the  same  horizontal  line  with 
the  minutes  the  azimuth  will  be  found  under  the  given  latitude,  which 
is  marked  at  the -top  of  the  right-hand  half  of  each  page.  Thus,  for 
1904,  time  argument  Oh  43m,  latitude  36°,  find  Oh  on  left-hand  page, 
and  under  1904  find  43m  on  tenth  line  from  the  top,  and  on  same  line 
with  the  minutes,  under  latitude  36°,  is  the  azimuth  0°  17'.  For  1908, 
time  argument  9h  33im,  latitude  48°,  the  azimuth  is  1°  Ij-',  found  on  the 
twenty-first  line  from  the  top  of  right-hand  page. 

If  the  exact  time  argument  is  not  found  in  the  table,  the  azimuth 
should  be  proportioned  to  the  difference  between  the  given  and  tabu- 
lar values  of  said  argument. 

The  table  has  been  arranged  to  give  the  azimuths  by  simple  inspec- 
tion. No  written  arithmetical  work  is  required,  all  being  performed 
mentally.  It  will  always  be  sufficient  to  take  the  nearest  whole  degree 
of  latitude  and  use  it  as  above  directed,  except  for  a  few  values  near 
the  top  of  either  page  where  the  difference  of  azimuths  for  2°  differ- 
ence of  latitude  amounts  to  four  or  five  minutes  of  arc. 

a  The  vertical  diameter  SS',  fig.  6,  divides  the  apparent  path  of  Polaris  into  two  equal  parts,  and  for 
the  star  at  any  point  Se  on  the  east  side  is  a  corresponding  point  st  on  the  west  side  of  the  meridian, 
for  which  azimuth  Nw  is  equal  to  the  azimuth  Ne.  The  arc,  Ss!  8%,  taken  from  the  entire  circle  (or 
23P  56*.!),  leaves  the  arc  Sse,  and  its  equal  Sslt  expressed  in  time,  may  be  used  to  find,  from  table  3, 
the  azimuth  Nw,  which  is  equal  to  Ne. 

The  hour  angles  entered  in  table  3  include  only  those  of  the  west  half  of  the  circle  ending  at  S, 
and  when  an  hour  angle  greater  than  llh  58m  results  from  observation  it  will  be  subtracted  from  23h 
66m.l,  and  the  remainder  will  be  used  as  the  "time  argument"  for  the  table.  The  surveyor  should 
not  confound  these  two  quantities.  The  hour  angle  itself  always  decides  the  direction  of  the  azimuth 
and  defines  the  place  of  the  star  with  reference  to  the  pole  and  meridian,  as  noted  at  top  of  table  3. 
See  examples. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  23 

The  attention  of  the  observer  is  directed  to  the  fact  that  he  should 
always  use  one  day  of  twenty-four  hours  as  the  unit  when  he  subtracts 
the  time  of  culmination  from  the  time  of  observation.  In  any  case 
when  the  time  of  upper  culmination,  taken  from  table  1,  for  the  given 
date  would  be  numerically  greater  than  the  astronomical  time  of 
observation,  the  former  time  will  be  taken  out  for  a  date  one  day 
earlier  than  the  date  of  observation.  The  surveyor  will  decide  when 
such  condition  exists  by  comparing  the  time  given  in  the  table  with 
his  astronomical  time  of  observation.  (See  Example  4  and  explana- 
tions in  footnotes,  page  24.) 

The  watch  time  to  be  used  when  making  observations  on  Polaris  at 
all  times  except  elongation  should  be  as  accurate  as  can  be  obtained. 
Looking  at  table  3  near  top  of  page  20,  the  surveyor  will  observe 
that  for  a  difference  of  four  minutes  in  the  time  argument  there  is  a 
change  of  about  two  minutes  in  azimuth;  consequently,  to  obtain  the 
azimuth  to  the  nearest  whole  minute  of  arc,  the  local  mean  time,  upon 
which  all  depends,  should  be  known  within  two  minutes.  When  the 
observer  uses  standard  railroad  time  he  will  correct  the  same  for  the 
difference  of  longitude  between  his  station  and  the  standard  meridian 
for  which  the  time  is  given  at  the  rate  of  four  minutes  of  time  for 
each  degree  of  the  difference  in  arc.  Thus,  if  the  difference  in  longi- 
tude is  6°  45',  the  equivalent  in  time  will  be  twenty-seven  minutes. 
The  difference  of  longitude  may  be  taken  from  a  good  map.  The  cor- 
rection will  be  subtracted  from  the  standard  railroad  time  of  observa- 
tion when  the  surveyor's  station  is  west,  or  added  when  east  of  the 
standard  meridian,  as  the  case  m&y  require,  to  obtain  local  time.  It  is 
immaterial  where  the  surveyor  obtains  the  standard  time  provided  he 
gets  it  right,  a  result  which  will  be  gained  most  easily  by  a  direct 
personal  comparison  at  a  telegraph  office. 

If  the  direction  of  the  meridian  is  known  with  an  error  not  greater 
than  one-fourth  of  a  degree,  the  local  time  can  be  obtained  to  the 
nearest  minute  by  observing  the  sun's  transit  by  the  following  method, 
suggested  by  Mr.  H.  L.  Baldwin,  jr. 

The  transit  being  in  meridian  and  carefully  leveled,  place  the  tele- 
scope so  that  it  will  point  toward  the  sun  at  the  time  the  latter  comes 
to  the  meridian  and  allow  the  magnified  image  of  the  sun  to  fall  upon 
a  notebook  or  sheet  of  white  paper  about  1  foot  distant  from  eyepiece. 
The  telescope  should  be  slightly  out  of  focus  (lengthened)  to  get  best 
results,  the  best  focal  position  to  be  determined  by  trial.  When  the 
vertical  cross  wire  bisects  the  sun's  image,  note  the  time  by  watch. 
This  will  be  the  time  of  apparent  noon.  To  get  time  of  mean  noon, 
correct  the  noted  time  by  adding  or  subtracting  the  equation  of  time, 
taken  from  the  Nautical  Almanac  uto  reduce  apparent  noon  to  mean 
noon,"  or  get  this  from  any  almanac  giving  "sun  fast"  or  "sun  slow" 
time. 


24  GEOGRAPHIC  TABLES  AND  FORMULAS. 

Example. 

June  20,  1903.  h.    m.  s. 

Watch  time  of  sun's  transit 11     50  25 

Equation  of  time +1  04 

Local  mean  noon 11     51    29 

Or  watch  slow 8    31 

The  error  of  observation  should  not  exceed  two  or  three  seconds 
and  the  error  resulting  from  incorrect  meridian  will  be  approximately 
four  seconds  for  each  1'  error  in  meridian. 

APPLICATIONS  OF  TABLES  1  AND  3. 

1.  Required  the  hour  angle  and  azimuth  of  Polaris,  for  a  station  in  latitude  46° 
N.,  longitude 90°  W.,  at  8h  24m  p.  m.,  November  7,  1910. 

h.       m. 

Astronomical  time  of  observation,  1910,  November  7 8    24.  0 

Equivalent  to  time  of  November  6 32    24.  0 

h.        m. 

Astron.  time,  TJ.  C.  Polaris,  November  1  (table  1) . .     10    45.  3 
Reduction  to  November  6  «  ( B ) ,  subtract &  19.  7 

Astron.  time,  U.  C.  Polaris,  November  6 10    25.  6,  subtract .  '10    25.  6 

Hour  angle  of  Polaris,  at  observation 21    58.  4 

Subtract  from..  ...  ^23    56.1 


Time  argument  for  table  3 1    57.  7 

Azimuth  of  Polaris,  at  observation 0°  51'  E. 

2.  Required  the  hour  angle  and  azimuth  of  Polaris,  for  a  station  in  latitude  4i° 
12'  N.,  longitude  94°  W.,  at  6h  16m  a.  m.,  November  19,  1904. 

h.         m. 

Astronominal  time  of  observation,  1904,  November  18 18     16. 0 

h.       m. 

Astron.  time,  U.  C.  Polaris,  November  15  (table  1) . .       9    47. 1 
Reduction  to  November  18,  subtract 11.  8 

Astron.  time,  U.  C.  Polaris,  November  18 9     35.  3,  subtract .       9     35.  3 

Hour  angle  of  Polaris,  at  observation,  and  time  argument  for  table  3 ^8    40.  7 

Azimuth  of  Polaris,  at  observation  (table  3) ,  72'  or fl°  12'  W. 

The  following  four  examples  illustrate  any  difficulties  in  the  use  of 
tables  1  and  3: 

a  By  reference  to  the  above  table,  the  surveyor  will  observe  that  the  times,  between  November  1 
and  15,  are  greater  than  8>>  24">;  consequently,  the  culmination  for  one  day  earlier,  November  6,  will 
be  used. 

bFrom  table  1,  opposite  sixth  day  of  month. 

c  To  subtract,  take  one  day  from  November  7,  and  add  its  equivalent,  24h,  to8h  24m,  making,  Novem- 
ber 6,  32h  24m  (which  is  the  time  expressed  by  November  7, 8h  24m);  then  subtract  in  the  usual  manner. 

dSee  last  clause  of  footnote,  page  22. 

«In  case  the  hour  angle  comes  out  greater  than  llh  58m,  subtract  it  from  23h  56m.l;  see  example  4, 
above. 

/The  hour  angle  being  less  than  11>>  58°>,  the  azimuth  is  west;  see  precepts?  top  of  table  3. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  25 

EVENING    OBSERVATIONS. 

1.  February  20,  1904,  at  7h  42m.5  p.  m.,  local  mean  time,  Polaris  is  observed  at  a 

station  in  southern  California,  latitude  36°,  longitude  117°. 

h.      m. 

Time  of  observation 7    42.  5 

h.       m. 

From  table  1,  U.  C.  Polaris,  February  15 3    45.  7 

Reduction  to  February  20 19.  7 

3     26. 0 


Time  elapsed  since  preceding  culmination 4    16.  5 

From  table  3  corresponding  azimuth  is  80/.5=1°  20'.5. 

2.  May  9,  1904,  at  8h  56m.4  p.  m.,  local  mean  time,  Polaris  is  observed  at  a  station  in 
northeastern  Minnesota,  latitude  48°,  longitude  90°.  The  nearest  culmination  is  that 
of  May  8. 

h.        m. 

Time  of  observation  May  9,  1904,  8h  56m.4,  or  May  8 32     56. 4 

h.       m. 

From  table  1,  U.  C.,  May  1,  1904 22    42.  7 

Reduction  to  May  8 27.  6 

22     15. 1 


Time  elapsed  since  preceding  culmination 10    41.  3 

From  table  3,  eorresponding  azimuth  is  34'. 

MORNING    OBSERVATIONS. 

3.  May  10,  1904,  at  5h  13m  a.  m.,  local  mean  time,  or  May  9,  17h  13m,  astronomical 
time,  Polaris  is  observed  at  a  station  in  northeastern  Minnesota,  latitude  ^8°, 
longitude  90°. 

h.       m. 

Time  of  observation,  May  9,  1904 17     13. 0 

h.         m. 

From  table  1,  U.  C.,  May  1 22    42.7 

Reduction  to  May  9 31. 5 

22     11.2 


Time  to  elapse  to  next  following  culmination 4    58.  2 

From  table  3  corresponding  azimuth  is  104'.3=1°  44'.  3 

4.  February  21, 1904,  at  5h  10m  a.  m.,  local  mean  time,  Polaris  is  observed  at  a  station 
in  southern  California,  latitude  36°,  longitude  117°.     The  nearest  culmination  is  on 

February  21. 

h.        m. 

Time  of  observation,  February  20 • 17     10.  0 

h.      m. 

From  table  1,  U.  C.,  February  15 3    45.7 

Reduction  to  February  20 19.  7 


h.       m. 


3    26.0+23    56.1=27    22.1 


Time  to  elapse  to  next  following  culmination 10     12. 1 

From  table  3,  corresponding  azimuth  is  39'.  3. 


26  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  4. — AZIMUTH  AND  APPARENT  ALTITUDE  OP  POLARIS  AT  DIFFERENT  HOUR  ANGLES. 
[From  U.  S.  Coast  and  Geodetic  Survey  Report  for  1895.] 

The  accompanying  tables  are  intended  for  field  use,  to  facilitate 
placing  an  instrument  in  the  meridian.  They  are  also  suitable  for 
determining  the  approximate  latitude  or  meridian.  They  contain  the 
azimuth  of  Polaris  at  intervals  of  fifteen  minutes  in  hour  angle  for 
each  degree  of  north  latitude  from  30°  to  60°,  and  the  apparent  alti- 
tude at  the  same  intervals  and  for  each  fifth  degree  of  latitude.®  The 
tables  are  computed  for  the  declination  of  Polaris  88°  46',  but  the  rate 
of  change  in  both  azimuth  and  altitude  is  given  with  the  argument  V 
increase  in  declination.6  The  tables  are  intended  to  be  used  in  con- 
nection with  the  American  Ephemeris,  where  are  given  the  apparent 
right  ascension  and  declination  of  Polaris  for  each  day  in  the  year. 
The  approximate  local  time  will  in  general  be  known  with  sufficient 
accuracy  from  standard  time  and  the  approximate  longitude  of  the 
place.  The  following  example  explains  the  use  of  the  tables  and  the 
derivation  of  the  hour  angle  of  Polaris: 

Position,  latitude  36°  20'  N.,  longitude  5h  20m  30s  W.  of  Greenwich. 

h.  m.  s. 

Time  of  observation,  July  10, 1895,  standard  (75th  mer. )  mean  time    8  52  40  p.  m. 

Reduction  to  local  time  —  20  30 


Local  mean  time  8  32  10 

Reduction  to  sidereal  time  (Table  III,  Amer.  Ephem. )  -f  1  24 

Sidereal  time  mean  noon,  Greenwich,  July  10, 1895  7  12  38 

Correction  for  longitude,  5h  20m  30s  (Table  III,  Amer.  Ephem.)  +  0  53 

Local  sidereal  time  15  47  05 

Apparent  right  ascension  of  Polaris,  July  10, 1895  1  20  18 


Hour  angle  before  upper  culmination  9    33    13 


a  The  tables  were  computed  with  the  following  formulas: 

sinj 

ten  a  =  cos.9~taiTfi  -  siiF^TcosY 

sin  h  =  sin  <p  sin  S  +  cos  <p  «os  8  cos  t, 

cos  5 

8111  a'=c^' 
cos  <e=cot  S  tan  <p; 

where  &  —  azimuth  from  true  north, 
t  —  hour  angle, 
g>  =  latitude, 
8  =  declination, 
h  =  true  altitude, 
ae  =  azimuth  at  elongation, 
te  —  hour  angle  at  elongation. 

b  As  the  corrections  are  given  with  proper  sign  for  increase  in  declination  over  88°  46',  they  are  to 
be  applied  with  reversed  sign  while  the  declination  is  less  than  88°  46',  as  it  will  be  until  near  the 
close  of  the  century. 


GEOGRAPHIC  TABLED 


FORMULAS. 


27 


Declination  of  table 

Apparent  declination,  July  10, 1895 

Increase  in  declination 


o         /  // 

88    46 

88    44  47 

-  1  13= 


Values  from  tables  (interpolated)  azimuth  0    54    12,  apparent  altitude  35    21.8 
Correction  for — 1'.2  increase  in  declination  +52  —1.0 


0    55    04 
East  of  north 


35    20.8 


It  is  to  be  remembered  that  Polaris  is  east  of  the  meridian  for  twelve 
hours  before  upper  culmination,  and  west  of  the  meridian  for  twelve 
hours  after.  By  setting  the  instrument  at  the  apparent  altitude  and 
sweeping-  near  the  meridian  Polaris  can  ordinarily  be  found  and  the 
instrument  placed  in  the  meridian  some  time  before  dark.  With 
transit  instruments  not  provided  with  horizontal  arc,  the  value  of  the 
azimuth  adjusting  screw  may  be  readily  determined  and  used. 

Without  the  American  Ephemeris  these  tables  may  be  conveniently 
used  for  obtaining  the  approximate  meridian  or  latitude,  in  connection 
with  Bulletin  14,  United  States  Coast  and  Geodetic  Survey, a  where 
are  given  the  approximate  mean  times  of  culminations  of  Polaris,  and 
the  mean  declinations  for  various  epochs. 

a  Approximate  Times  of  Culminations  and  Elongations  and  of  the  Azimuths  at  Elongation  of  Polaris 
for  the  Years  between  1889  and  1910. 
The  mean  places  of  Polaris  are  given  as  follows: 


a 

£ 

1895  .  .  . 

h.  m.   8. 
1  20  30.08 

0     /     // 

88  44  6268 

1900  

1  22  33  76 

88  46  26  66 

1905 

1  24  42  48 

88  48  00  31 

1910  

1  26  56.58 

88  49  33  61 

28 


GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  4. — Azimuth  and  apparent  altitude 


Hour  angle  before 
or  after  upper 
culmination. 

Azimuth  of  Polaris  computed  for  declination  88°  46'. 

Latitude 
30°. 

Latitude 
31°. 

Latitude 
32°. 

Latitude 
33°. 

Latitude 
34°. 

Latitude 
35°. 

h.  m. 
0  15 

0  05  40 

0  05  43 

0  05  47 

0  05  51 

0  05  55 

0  06  00 

0  30 

0  11  18 

0  11  25 

0  11  33 

0  11  41 

0  11  49 

0  11  58 

0  45 

0  16  53 

0  17  04 

0  17  15 

0  17  27 

0  17  40 

0  17  53 

1  00 

0  22  23 

0  22  38 

0  22  53 

0  23  09 

0  23  26 

0  23  44 

1  15 

0  27  48 

0  28  06 

0  28  25 

0  28  45 

0  29  06 

0  29  28 

1  30 

0  33  05 

0  33  26 

0  33  49 

0  34  13 

0  34  38 

0  35  04 

1  45 

0  38  13 

0  38  38 

0  39  04 

0  39  32 

0  40  00   0  40  30 

2  00 

0  43  12 

0  43  40 

0  44  09 

0  44  40 

0  45  12  !  0  45  46 

2  15 

0  47  58 

0  48  29 

0  49  02 

0  49  36 

0  50  12   0  50  50 

2  30 

0  52  32 

0  53  06 

0  53  42 

0  54  19 

0  54  59 

0  55  40 

2  45 

0  56  52 

0  57  29 

0  58  07 

0  58  48 

0  59  30 

1  00  15 

3  00 

1  00  58 

1  01  37 

1  02  18 

1  03  01 

1  03  46   1  04  34 

3  15 

1  04  47 

1  05  28 

1  06  12 

1  06  58 

1  07  46 

1  08  36 

3  30 

08  19 

1  09  02 

1  09  48 

1  10  36 

1  11  27 

1  12  20 

3  45 

11  33 

1  12  18 

1  13  06 

1  13  56 

1  14  49 

1  15  45 

4  00 

14  28 

1  15  15 

1  16  05 

1  16  57 

1  17  52 

1  18  50 

4  15 

17  04 

1  17  52 

1  18  44 

1  19  37 

1  20  34 

1  21  34 

4  30 

19  19 

1  20  09 

1  21  02 

1  21  57 

1  22  55 

1  23  57 

4  45 

21  14 

1  22  05 

1  22  59 

1  23  55 

1  24  55 

1  25  57 

5  00 

22  48 

1  23  40 

1  24  35 

1  25  32 

1  26  32 

1  27  36 

5  15 

24  08 

1  24  53 

1  25  48 

1  26  46 

1  27  47 

1  28  51 

5  30 

24  51 

1  25  44 

1  26  40 

1  27  38 

1  28  39 

1  29  44 

5  45 

25  20 

1  26  13 

1  27  09 

1  28  07 

1  29  09 

1  30  14 

6  00 

25  27 

1  26  19 

1  27  15 

1  28  14 

1  29  15 

1  30  20 

6  15 

25  12 

1  26  04 

1  26  59 

1  27  57 

1  28  59 

1  30  03 

6  30 

24  34 

1  25  27 

1  26  21 

1  27  19 

1  28  19 

1  29  23 

6  45 

23  36 

1  24  27 

1  25  21 

1  26  18 

1  27  17 

1  28  20 

7  00 

22  16 

1  23  06 

1  23  59 

1  24  55 

1  25  53 

1  26  55 

7  15 

20  35 

1  21  25 

1  22  16 

1  23  10 

1  24  08 

1  25  08 

7  30 

18  34 

1  19  22 

1  20  12 

1  21  05 

1  22  00 

1  22  59 

7  45 

16  13 

1  16  59 

1  17  48 

1  18  39 

1  19  33 

1  20  29 

8  00 

13  33 

1  14  17 

1  15  04 

1  15  53 

1  16  45 

1  17  39 

8  15 

10  34 

1  11  16 

1  12  01 

1  12  48 

1  13  37 

1  14  29 

8  30 

1  07  17 

1  07  57 

1  08  40 

1  09  25 

1  10  12 

1  11  01 

8  45 

1  03  43 

1  04  22 

1  05  02 

1  05  44 

1  06  29 

1  07  15 

9  00 

0  59  54 

1  00  30 

1  01  07 

1  01  47 

1  02  29 

1  03  12 

9  15 

0  55  49 

0  56  23 

0  56  58 

0  57  34 

0  58  13 

0  58  54 

9  30 

0  51  31 

0  52  01 

0  52  34 

0  53  08 

0  53  43 

0  54  21 

9  45 

0  46  59 

0  47  27 

0  47  57 

0  48  28 

0  49  00 

0  49  34 

10  00 

0  42  16 

0  42  42 

0  43  08 

0  43  36 

0  44  05 

0  44  35 

10  15 

0  37  23 

0  37  45 

0  38  08 

0  38  33 

0  38  59 

0  39  26 

10  30 

0  32  20 

0  32  39 

0  32  59 

0  33  20 

0  33  43 

0  34  06 

10  45 

0  27  09 

0  27  25 

0  27  42 

0  28  00 

0  28  18 

0  28  38 

11  00 

0  21  51 

0  22  04 

0  22  18 

0  22  32 

0  22  47 

0  23  03 

11  15 

0  16  28 

0  16  38 

0  16  .48 

0  16  59 

0  17  10 

0  17  22 

11  30 

0  11  01 

0  11  08 

0  11  14 

0  11  22 

0  11  29 

0  11  37 

11  45 

0  05  31 

0  05  34 

0  05  38 

0  05  42 

0  05  45 

0  05  49 

Elongation  : 
Azimuth  .  .  . 

1  25  27 

1  26  20 

1  27  16 

1  28  14 

1  29  16 

1  30  20 

h.  m.  s. 

h.  m.  8. 

//.  m.  s. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

Hour  angle. 

5  57  09 

5  57  02 

5  56  55 

5  56  48 

5  56  40 

5  56  33 

GEOGRAPHIC   TABLES    AND   FOEMULA8. 

of  Polaris  at  different  hour  angles. 


29 


Azimuth  of  Polaris  computed  for  declination  88°  46'. 

Correction  for  1'  in- 
crease in  declina- 
tion of  Polaris. 

Hour 
angle 
before 
or  after 
upper 
culmi- 
nation. 

Latitude 
36°. 

Latitude 
37°. 

Latitude 
38°. 

Latitude 
39°. 

Latitude 
40°. 

Latitude 
30°. 

Latitude 
40°. 

0  06  05 

0  06  10 

0  06  15 

0  06  20 

0  06  26 

-  5 

// 

-  5 

h.  TO. 
0  15 

0  12  08 

0  12  18 

0  12  28 

0  12  39 

0  12  50 

g 

-10 

0  30 

0  18  07 

a  is  22 

0  18  38 

0  18  54 

0  19  11 

—14 

-16 

0  45 

0  24  02 

0  24  22 

0  24  43 

0  25  04 

0  25  27 

-18 

—21 

1  00 

0  29  51 

0  30  15 

0  30,  41 

0  31  08 

0  31  36 

-23 

—26 

1  15 

0  35  31 

0  36  00 

0  36  31 

0  37  02 

0  37  36 

—27 

-31 

1  30 

0  41  02 

0  41  35 

0  42  11 

0  42  47 

0  43  26 

—31 

-36 

1  45 

0  46  22 

0  47  00 

0  47  39 

0  48  21 

0  49  04 

—35 

-40 

2  00 

0  51  29 

0  52  11 

0  52  55 

0  53  41 

0  54  29 

-39 

—45 

2  15 

0  56  23 

0  57  09 

0  57  57 

0  58  47 

0  59  40 

-43 

-49 

2  30 

1  01  02 

1  01  51 

1  02  43 

1  03  37 

1  04  34 

-46 

-53 

2  45 

1  05  24 

1  06  17 

1  07  12 

1  08  10 

1  09  12 

—50 

-57 

3  00 

1  09  29 

1  10  25 

1  11  24 

1  12  25 

1  13  30 

-53 

-60 

3  15 

1  13  16 

1  14  14 

1  15  16 

1  16  21 

1  17  29 

-56 

-63 

3  30 

1  16  43 

1  17  44 

1  18  49 

1  19  57 

1  21  08 

-58 

-66 

3  45 

1  19  50 

1  20  54 

1  22  01 

1  23  11 

1  24  25 

-61 

-69 

4  00 

1  22  36 

1  23  42 

1  24  51 

1  26  03 

1  27  20 

—63 

—72 

4  15 

1  25  01 

1  26  08 

1  27  19 

1  28  33 

1  29  52 

—64 

—74 

4  30 

1  27  03 

1  28  12 

1  29  24 

1  30  40 

1  32  00 

—66 

—75 

4  45 

1  28  42 

1  29  52 

1  31  06 

1  32  23 

1  33  44 

-68 

-76 

5  00 

1  29  59 

1  31  09 

1  32  24 

1  33  42 

1  35  04 

-69 

-77 

5  15 

1  30  52 

1  32  03 

1  33  18   1  34  37 

1  35  59 

-69 

-78 

5  30 

1  31  21 

1  32  33 

]  33  48  |  1  35  07 

1  36  30 

—70 

—78 

5  45 

1  31  27 

1  32  39 

1  33  54   1  35  13 

1  36  35 

-70 

—78 

6  00 

1  31  10 

1  32  21 

1  33  36 

1  34  54 

1  36  16 

-69 

-78 

6  15 

1  30  30 

1  31  40 

1  32  54 

1  34  11 

1  35  32 

-68 

-77 

6  30 

1  29  26 

1  30  35 

1  31  48 

1  33  04 

1  34  24 

—67 

—76 

6  45 

1  27  59 

1  29  07 

1  30  18 

1  31  33 

1  32  52 

-66 

—75 

7  00 

1  26  11 

1  27  17 

1  28  26 

1  29  39 

1  30  56 

-65 

-73 

7  15 

1  24  00 

1  25  04 

1  26  12 

1  27  23 

1  28  38 

-64 

-72 

7  30 

1  21  28 

1  22  30 

1  23  36 

1  24  45 

25  57 

—62 

-69 

7  45 

1  18  36 

1  19  36 

1  20  39 

1  21  45 

22  54 

—60 

-66 

8  00 

1  15  24 

1  16  21 

1  17  22 

1  18  25 

19  31 

-57 

-64 

8  15 

1  11  53 

1  12  48 

1  13  45 

1  14  45 

15  48 

-54 

-61 

8  30 

1  08  04 

1  08  56 

1  09  50 

1  10  47 

11  47 

—51 

-58 

8  45 

1  03  58 

1  04  47 

1  05  38 

1  06  31 

07  27 

-48 

—54 

9  00 

0  59  37 

1  00  22 

1  01  09 

1  01  59 

02  51 

-45 

-50 

9  15 

0  55  00 

0  55  42 

0  56  25 

0  57  11 

0  57  59 

-42 

-46 

9  30 

0  50  10 

0  50  48 

0  51  27 

0  52  09 

0  52  53 

-38 

-42 

9  45 

0  45  08 

0  45  42 

0  46  17 

0  46  54 

0  47  34 

—34 

-38 

10  00 

0  39  54 

0  40  24 

0  40  55 

0  41  28 

0  42  03 

-30 

-34 

10  15 

0  34  30 

0  34  57 

0  35  24 

0  35  52 

0  36  22 

-26 

-29 

10  30 

0  28  59 

0  29  20 

0  29  43 

0  30  07 

0  30  32 

-22 

-24 

10  45 

0  23  19 

0  23  37 

0  23  55 

0  24  14 

0  24  35 

—18 

-20 

11  00 

0  17  35 

0  17  48 

0  18  02 

0  18  16 

0  18  31 

—13 

—15 

1JL  15 

0  11  46 

0  11  54 

0  12  04 

0  12  13 

0  12  23 

-  9 

-10 

11  30 

0  05  53 

0  05  58 

0  06  02 

0  06  07 

0  06  12 

-  4 

-  5 

11  45 

1  31  28 

1  32  40 

1  33  55 

1  35  14 

1  36  36 

-69 

-78 

h.  m.  s. 

h.  m.  s. 

h.  TO.  8. 

h.  TO.  8. 

h.  TO.  8. 

8. 

8. 

5  56  25 

5  56  17 

5  56  09 

5  56  00 

5  55  52 

+  2 

+  3 

30 


GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  4. — Azimuth  and  apparent  altitude 


Azimuth  of  Polaris  computed  for  declination  88°  46'. 

Hour  angle  before 

or  after  upper 

elimination. 

Latitude 

Latitude 

Latitude 

Latitude 

Latitude 

Latitude 

40°. 

41°. 

42°. 

43°. 

44°. 

45°. 

h.  m. 
0  15 

0  06  26 

0  06  32 

0  06  39 

0  06  45 

0  06  52 

0  07  00 

0  30 

0  12  50 

0  13  03 

0  13  15 

0  13  29 

0  13  43 

0  13  58 

0  45 

0  19  11 

0  19  30 

0  19  48 

0  20  08 

0  20  29 

0  20  52 

1  00 

0  25  27 

0  25  51 

0  26  16 

0  26  43 

0  27  10 

0  27  40 

1  15 

0  31  36 

0  32  05 

0  32  36 

0  33  09 

0  33  44 

0  34  21 

1  30 

0  37  36 

0  38  11 

0  38  48 

0  39  27 

0  40  09 

0  40  52 

1  45 

0  43  26 

0  44  07 

0  44  50 

0  45  35 

0  46  22 

0  47  12 

2  00 

0  49  04 

0  49  50 

0  50  39 

0  51  29 

0  52  23 

0  53  19 

2  15 

0  54  29 

0  55  20 

0  56  14 

0  57  10 

0  58  10 

0  59  12 

2  30 

0  59  40 

1  00  35 

1  01  34 

1  02  36 

1  03  41 

1  04  49 

2  45 

1  04  34 

1  05  34 

1  06  38 

1  07  44 

1  08  54 

1  10  08 

3  00 

1  09  12 

1  10  16 

1  11  24 

1  12  35 

1  13  50 

1  15  09 

3  15 

1  13  30 

1  14  38 

1  15  50 

1  17  06 

1  18  25 

1  19  49 

3  30 

1  17  29 

1  18  41 

1  19  57 

1  21  16 

1  22  39 

1  24  08 

3  45 

1  21  08 

1  22  23 

1  23  42 

1  25  04 

1  26  32 

1  28  04 

4  00 

1  24  25 

1  25  43 

1  27  05 

1  28  31 

1  30  01 

1  31  37 

4  15 

1  27  20 

1  28  40 

1  30  04 

1  31  33 

1  33  07 

1  34  45 

4  30 

1  29  52 

1  31  14 

1  32  41 

1  34  12 

1  35  48 

1  37  29 

1  4  45 

1  32  00 

1  33  24 

1  34  53 

1  36  25 

1  38  04 

1  39  47 

5  00 

1  33  44 

1  35  10 

1  36  40 

1  38  14 

1  39  54 

1  41  38 

5  15 

1  35  04 

1  36  30 

1  38  02 

1  39  37 

1  41  18 

1  43  04 

5  30 

1  35  59 

1  37  26 

1  38  58 

1  40  34 

1  42  16 

1  44  02 

5  45 

1  36  30 

1  37  57 

1  39  29 

1  41  05 

1  42  47 

1  44  34 

6  00 

1  36  35 

1  38  02 

1  39  34 

1  41  10 

1  42  51 

1  44  38 

6  15 

1  36  16 

1  37  43 

1  39  14 

1  40  49 

1  42  30 

1  44  16 

6  30 

1  35  32 

1  36  58 

1  38  28 

1  40  03 

1  41  42 

1  43  27 

6  45 

1  34  24 

1  35  48 

1  37  17 

1  38  50 

1  40  28 

1  42  12 

7  00 

1  32  52 

1  34  15 

1  35  42 

1  37  13 

1  38  49 

1  40  31 

7  15 

1  30  56 

1  32  17 

1  33  42 

1  35  11 

1  36  45 

1  38  24 

7  30 

1  28  38 

1  29  56 

1  31  19 

1  32  46 

1  34  17 

1  35  53 

7  45 

1  25  57 

1  27  13 

1  28  33 

1  29  56 

1  31  25 

1  32  58 

8  00 

1  22  54 

1  24  07 

1  25  24 

1  26  45 

1  28  10 

1  29  40 

8  15 

1  19  31 

1  20  41 

1  21  55 

1  23  12 

1  24  33 

1  25  59 

8  30 

1  15  48 

1  16  55 

1  18  05 

1  19  18 

1  20  35 

1  21  57 

8  45 

1  11  47 

1  12  49 

1  13  55 

1  15  05 

1  16  18 

1  17  35 

9  00 

1  07  27 

1  08  26 

1  09  28 

1  10  33 

1  11  41 

1  12  54 

9  15 

1  02  51 

1  03  45 

1  04  43 

1  05  43 

1  06  47 

1  07  54 

9  30 

0  57  59 

0  58  49 

0  59  42 

1  00  38 

1  01  37 

1  02  38 

9  45 

0  52  53 

0  53  39 

0  54  27 

0  55  18 

0  56  11 

0  57  07 

10  00 

0  47  34 

0  48  15 

0  48  58 

0  49  44 

0  50  32 

0  51  22 

10  15 

0  42  03 

0  42  39 

0  43  18 

0  43  58 

0  44  40 

0  45  25 

10  30 

0  36  22 

0  36  53 

0  37  26 

0  38  01 

0  38  38 

0  39  16 

10  45 

0  30  32 

0  30  58 

0  31  26 

0  31  55 

0  32  26 

0  32  58 

11  00 

0  24  35 

0  24  56 

0  25  18 

0  25  42 

0  26  06 

0  26  32 

.   11  15 

0  18  31 

0  18  47 

0  19  04 

0  19  22 

0  19  40 

0  20  00 

11  30 

0  12  23 

0  12  34 

0  12  45 

0  12  57 

0  13  09 

0  13  23 

11  45 

0  06  12 

0  06  18 

0  06  23 

0  06  29 

0  06  36 

0  06  42 

Elongation: 
Azimuth  .  .  . 

1  36  36 

1  38  03 

1  39  35 

1  41  11 

1  42  53 

1  44  40 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

Hour  angle  . 

5  55  52 

5  55  43 

5  55  34 

5  55  24 

5  55  14 

5  55  04 

GEOGEAPHIC    TABLES    AND    FORMULAS. 
of  Polaris  at  different  hour  angles — Continued. 


31 


Correction  for  1'  in- 

TTrtiiT 

Azimuth  of  Polaris  computed  for  declination  88°  46'. 

crease  in  declina- 

Hour 
angle 

tion  of  Polaris. 

before 

or  after 

Latitude 

Latitude 

Latitude 

Latitude 

Latitude 

Latitude 

Latitude 

upper 
culmi- 

46°. 

47°. 

48°. 

49°. 

50°. 

40°. 

50°. 

nation. 

0  07  08 

0  07  16 

0  07  25 

0  07  34 

0  07  44 

-  5 

—  6 

h.  m. 
0  15 

0  14  13 

0  14  30 

0  14  48 

0  15  06 

0  15  25 

-10 

-13 

0  30 

0  21  15 

0  21  40 

0  22  06 

0  22  33 

0  23  02 

—16 

-19 

0  45 

0  28  11 

0  28  44 

0  29  18 

0  29  55 

0  30  33 

—21 

-25 

1  00 

0  34  59 

0  35  40 

0  36  23 

0  37  08 

0  37  56 

-26 

—32 

1  15 

0  41  38 

0  42  26 

0  43  17 

0  44  11 

0  45  08 

-31 

-38 

1  30 

0  48  05 

0  49  01 

0  49  59 

0  51  02 

0  52  07 

-36 

-43 

1  45 

0  54  19 

0  55  22 

0  56  28 

0  57  38 

0  58  52 

—40 

-49 

2  00 

1  00  18 

1  01  28 

1  02  41 

1  03  59 

1  05  21 

—45 

-54 

2  15 

1  06  01 

1  07  17 

1  08  38 

1  10  03 

1  11  32 

-49 

—59 

2  30 

1  11  26 

1  12  48 

1  14  15 

1  15  47 

1  17  24 

-53 

-64 

2  45 

1  16  32 

1  18  00 

1  19  33 

1  21  11 

1  22  54 

-57 

-68 

3  00 

1  21  17 

1  22  50 

1  24  29 

1  26  13 

1  28  02 

-60 

-72 

3  15 

1  25  40 

1  27  18 

1  29  02 

1  30  51 

1  32  46 

-63 

-76 

•  3  30 

1  29  41 

1  31  23 

1  33  11 

1  35  05 

1  37  06 

-66 

—80 

3  45 

33  17 

1  35  03 

36  55 

1  38  54 

1  40  59 

-69 

-83 

4  00 

36  29 

1  38  18 

40  14 

1  42  16 

1  44  25 

-72 

-86 

4  15 

39  15 

1  41  08 

43  06 

1  45  11 

1  47  24 

-74 

-88 

4  30 

41  35 

1  43  30 

45  31 

1  47  39 

1  49  54 

-75 

-90 

4  45 

43  29 

1  45  25 

47  28 

1  49  38 

1  51  55 

-76 

-91 

5  00 

44  55 

1  46  53 

48  57 

1  51  08 

1  53  27  ' 

—77 

-92 

5  15 

45  54 

1  47  53 

49  58 

1  52  10 

1  54  30 

-78 

-93 

5  30 

46  26 

1  48  25 

50  30 

1  52  43 

1  55  03 

-78 

-94 

5  45 

46  31 

1  48  29 

50  34 

1  52  46 

1  55  06 

-78 

-93 

6  00 

1  46  08 

1  48  05 

1  50  10 

1  52  21 

1  54  40 

—78 

-93 

6  15 

1  45  18 

1  47  14 

1  49  17 

1  51  27 

1  53  44 

-77 

-92 

6  30 

1  44  01 

1  45  56 

1  47  56 

1  50  04 

1  52  20 

-76 

-91 

6  45 

1  42  18 

1  44  10 

1  46  09 

1  48  14 

1  50  27 

—75 

-89 

7  00 

1  40  09 

1  41  59 

1  43  54 

1  45  57 

1  48  06 

—73 

—87 

7  15 

1  37  35 

1  39  21 

1  41  14 

1  43  13 

1  45  19 

-72 

-85 

7  30 

1  34  36 

1  36  19 

1  38  08 

1  40  03 

1  42  05 

-69 

-82 

7  45 

1  31  14 

1  32  53 

1  34  38 

1  36  29 

1  38  26 

-66 

-79 

8  00 

1  27  29 

1  29  04 

1  30  44 

1  32  30 

1  34  22 

-64 

-76 

8  15 

1  23  23 

1  24  53 

1  26  28 

1  28  09 

1  29  55 

-61 

-72 

8  30 

1  18  56 

1  20  21 

1  21  51 

1  23  26 

1  25  07 

-58 

-68 

8  45 

1  14  10 

1  15  30 

1  16  54 

1  18  23 

1  19  57 

-54 

-64 

9  00 

1  09  05 

1  10  19 

1  11  38 

1  13  01 

1  14  28 

-50 

-59 

9  15 

1  03  44 

1  04  52 

1  06  04 

1  07  21 

1  08  41 

-46 

-55 

9  30 

0  58  07 

0  59  09 

1  00  15 

1  01  24 

1  02  38 

-42 

-50 

9  45 

0  52  16 

0  53  12 

0  54  11 

0  55  13 

0  56  19 

-38 

-45 

10  00 

0  46  12 

0  47  01 

0  47  53 

0  48  49 

0  49  47 

—34 

-40 

10  15 

0  39  57 

0  40  40 

0  41  25 

0  42  12 

0  43  02 

-29 

-34 

10  30 

0  33  32   0  34  08 

0  34  46 

0  35  26 

0  36  08 

-24 

-29 

10  45 

0  27  00  :  0  27  28 

0  27  59 

0  28  31 

0  29  05 

-20 

-23 

11  00 

0  20  20 

0  20  42 

0  21  05 

0  21  29 

0  21  55 

-15 

-18 

11  15 

0  13  36 

0  13  51 

0  14  06 

0  14  22 

0  14  39 

-10 

-12 

11  30 

0  06  49 

0  06  56 

0  07  04 

0  07  12 

0  07  21 

-  5 

—  6 

11  45 

1  46  32 

1  48  31 

1  50  36 

1  52  48 

1  55  08 

—78 

—93 

h.  m.  s. 

h.  m.  8. 

h.  m.  s. 

h.  m.  a. 

h.  m.  s. 

8. 

8. 

5  54  53 

5  54  42 

5  54  31 

5  54  20 

5  54  07 

+  3 

+  5 

32 


GEOGEAPHIC    TABLES    AND    FORMULAS. 

TABLE  4. — Azimuth  and  apparent  altitude 


Hour  angle  before 
or  after  upper 
culmination. 

Azimuth  of  Polaris  computed  for  declination  88°  46'. 

Latitude 
60°. 

Latitude 
51°. 

Latitude 
52°. 

Latitude 
53°. 

Latitude 

64°. 

Latitude 

55°. 

h.  m. 

0  15 

0  07  44 

0  07  54 

0  08  05 

0  08  17 

0  08  29 

0  08  42 

0  30 

0  15  25 

0  15  46 

0  16  08 

0  16  31 

0  16  56 

0  17  22 

0  45 

0  23  02 

0  23  33 

0  24  06 

0  24  41 

0  25  18 

0  25  57 

1  00 

0  30  33 

0  31  14 

0  31  58 

0  32  44 

6  33  33 

0  34  25 

1  15 

0  37  56 

0  38  47 

0  39  40 

0  40  38 

0  41  38 

0  42  43 

1  30 

0  45  08 

0  46  08 

0  47  12 

0  48  20 

0  49  32 

0  50  49 

1  45 

0  52  07 

0  53  17 

0  54  31 

0  55  49 

0  57  12 

0  58  41 

2  00 

0  58  52 

1  00  11 

1  01  34 

1  03  03 

1  04  37 

1  06  16 

2  15 

1  05  21 

1  06  48 

1  08  21 

1  09  59 

1  11  43 

1  13  33 

2  30 

1  11  32 

1  13  08 

1  14  48 

1  16  35 

1  18  29 

1  20  30 

2  45 

1  17  24 

1  19  07 

1  20  55 

1  22  51 

1  24  54 

1  27  04 

3  00 

1  22  54 

1  24  44 

1  26  41 

1  28  44 

1  30  55 

1  33  15 

3  15 

1  28  02 

1  29  59 

1  32  02 

1  34  13 

1  36  32 

1  39  00 

•  3  30 

1  32  46 

1  34  49 

1  36  58 

1  39  16 

1  41  42 

1  44  18 

3  45 

1  37  06 

1  39  14 

1  41  29 

1  43  52 

1  46  25 

1  49  07 

4  00 

1  40  59 

1  43  12 

1  45  32 

1  48  01 

1  50  39 

1  53  27 

4  15 

]  44  25 

1  46  42 

1  49  07 

1  51  40 

1  54  23 

1  57  16 

4  30 

1  47  24 

1  49  44 

1  52  13 

1  54  50 

1  57  37 

2  00  35 

4  45 

1  49  54 

1  52  17 

1  54  49 

1  57  29 

2  00  20 

2  03  21 

5  00 

1  51  55 

1  54  21 

1  56  54 

1  59  37 

2  02  31 

2  05  35 

5  15 

1  53  27 

1  55  54 

1  58  29 

2  01  15 

2  04  10 

2  07  16 

5  30 

1  54  30 

1  56  58 

1  59  34 

2  02  20 

2  05  16 

2  08  23 

5  45 

1  55  03 

1  57  31 

2  00  08 

2  02  53 

2  05  50 

2  08  58 

6  00 

1  55  06 

1  57  34 

2  00  10 

2  02  56 

2  05  52 

2  08  58 

6  15 

1  54  40 

1  57  06 

1  59  41 

2  02  26 

2  05  21 

2  08  26 

6  30 

1  53  44 

1  56  09 

1  58  43 

2  01  25 

2  04  18 

2  07  22 

6  45 

1  52  20 

1  54  42 

57  14 

1  59  54 

2  02  44 

2  05  45 

7  00 

1  50  27 

1  52  47 

55  15 

1  57  52 

2  00  39 

2  03  36 

7  15 

1  48  06 

1  50  23 

52  48 

1  55  21 

1  58  04 

2  00  57 

7  30 

1  45  19 

1  47  32 

49  52 

1  52  21 

1  54  59 

1  57  47 

7  45 

1  42  05 

44  13 

46  29 

1  48  53 

1  51  26 

1  54  08 

8  00 

38  26 

40  29 

42  40 

1  44  58 

1  47  25 

1  50  01 

8  15 

34  22 

36  20 

1  38  25 

1  40  38 

1  42  58 

1  45  27 

8  30 

29  55 

31  48 

1  33  47 

1  35  52 

1  38  06 

1  40  28 

8  45 

25  07 

26  53 

1  28  45 

1  30  44 

1  32  50 

1  35  04 

9  00 

19  5r 

1  21  37 

1  23  22 

1  25  13 

1  27  11 

1  29  17 

9  15 

14  28 

1  16  01 

1  17  38 

1  19  22 

1  21  12 

1  23  08 

9  30 

08  41 

1  10  06 

1  11  36 

1  13  12 

1  14  53 

1  16  40 

9  45 

1  02  38 

1  03  55 

1  05  17 

1  06  44 

1  08  16 

1  09  53 

10  00 

0  56  19 

0  57  28 

0  58  42 

1  00  00 

1  01  23 

1  02  50 

10  15 

0  49  47 

0  50  48 

0  51  53 

0  53  02 

0  54  15 

0  55  32 

10  30 

0  43  02 

0  43  56 

0  44  52 

0  45  51 

0  46  54 

0  48  01 

10  45 

0  36  08 

0  36  52 

0  37  39 

0  38  29 

0  39  22 

0  40  18 

11  00 

0  29  05 

0  29  41 

0  30  18 

0  30  58 

0  31  41 

0  32  26 

11  15 

0  21  55 

0  22  22 

0  22  50 

0  23  20 

0  23  52 

0  24  26 

11  30 

0  14  39 

0  14  57 

0  15  16 

0  15  37 

0  15  58 

0  16  21 

11  45 

0  07  21 

0  07  30 

0  07  39 

0  07  49 

0  08  00 

0  08  11 

Elongation: 
Azimuth  

1  55  08 

1  57  36 

2  00  13 

2  Q2  59 

2  05  55 

2  09  02 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

h.  m.  e. 

h.  m.  8. 

h.  m.  s. 

Hour  angle. 

5  54  07 

5  53  54 

5  53  41 

5  53  27 

5  53  12 

5  52  57 

^S  GEOGRAPHIC   TABLES    AND   FORMULAS. 

of  Polaris  at  different  hour  angles — Continued. 


33 


Azimuth  of  Polaris  computed  for  declination  88°  46'. 

Correction  for  1'  in- 
crease in  declina- 
tion of  Polaris. 

Hour 
angle 
before 
or  after 
upper 
culmi- 
nation. 

Latitude 
56°. 

Latitude 

57°. 

Latitude 
58°. 

Latitude 
59° 

Latitude 
60°. 

Latitude 
50°. 

Latitude 
60°. 

o   /   /> 

o   /   // 

0    /    II 

O    '    // 

Of" 

// 

„ 

h.  TO. 

0  08  56 

0  09  12 

0  09  28 

0  09  45 

0  10  03 

-6 

-  8 

0  15 

0  17  50 

0  18  20 

0  18  53 

0  19  27 

0  20  04 

-13 

-  17 

0  30 

0  26  39 

0  27  24 

0  28  12 

0  29  03 

0  29  58 

—19 

—  25 

0  45 

0  35  21 

0  36  20 

0  37  23 

0  38  31 

0  39  44 

—25 

-  33 

1  00 

0  43  52 

0  45  06 

0  46  24 

0  47  48 

0  49  19 

-32 

-  41 

1  15 

0  52  11 

0  53  39 

0  55  12 

0  56  52 

0  58  40 

-38 

-  49 

1  30 

1  00  16 

1  01  56 

1  03  44 

1  05  40 

1  07  44 

-43 

-  57 

1  45 

1  08  03 

1  09  57 

1  11  58 

1  14  08 

1  16  28 

—49 

-  64 

2  00 

1  15  31 

1  17  37 

1  19  52 

1  22  16 

24  51 

—54 

-  71 

2  15 

1  22  39 

1  24  56 

1  27  24 

1  30  01 

32  50 

-59 

-  78 

2  30 

1  29  23 

1  31  52 

1  34  31 

1  37  21 

40  23 

-64 

-  84 

2  45 

1  35  43 

1  38  22 

1  41  12 

]  44  13 

47  28 

—68 

-  89 

3  00 

1  41  37 

1  44  25 

1  47  25 

1  50  37 

54  03 

—72 

-  94 

3  15 

1  47  03 

1  50  00 

1  53  08 

1  56  30 

2  00  07 

-76 

-  99 

3  30 

1  52  00 

1  55  04 

1  58  21 

2  01  51 

2  05  37 

-80 

-104 

3  45 

1  56  26 

1  59  37 

2  03  01 

2  06  40 

2  10  34 

-83 

—108 

4  00 

2  00  21 

2  03  38 

2  07  09 

2  10  54 

2  14  55 

—86 

—111 

4  15 

2  03  44 

2  07  06 

2  10  42 

2  14  32 

2  18  39 

—88 

—114 

4  30 

2  06  34 

2  10  00 

2  13  40 

2  17  35 

2  21  47 

—90 

-116 

4  45 

2  08  51 

2  12  20 

2  16  03 

2  20  02 

2  24  17 

-91 

-118 

5  00 

2  10  34 

2  14  05 

2  17  50 

2  21  51 

2  26  09 

-92 

—119 

5  15 

2  11  42 

2  15  14 

2  19  01 

2  23  04 

2  27  23 

-93 

-120 

5  30 

2  12  17 

2  15  50 

2  19  36 

2  23  39 

2  27  58 

—94 

-120 

5  45 

2  12  17 

2  15  49 

2  19  35 

2  23  37 

2  27  56 

—93 

-120 

6  00 

2  11  44 

2  15  14 

2  18  59 

2  22  59 

2  27  15 

-93 

-119 

6  15 

2  10  37 

2  14  05 

2  17  47 

2  21  44 

2  25  57 

-92 

—118 

6  30 

2  08  57 

2  12  21 

2  16  00 

2  19  53 

2  24  03 

—91 

—116 

6  45 

2  06  44 

2  10  05 

2  13  39 

2  17  27 

2  21  32' 

—89 

—114 

7  00 

2  04  00 

2  07  16 

2  10  45 

2  14  27 

2  18  26 

-87 

—111 

7  15 

2  00  45 

2  03  55 

2  07  18 

2  10  54 

2  14  46 

-85 

—108 

7  30 

1  57  00 

2  00  04 

2  03  20 

2  06  49 

2  10  32 

-82 

—104 

7  45 

1  52  47 

1  55  43 

1  58  52 

2  02  12 

2  05  47 

—79 

-100 

8  00 

1  48  06 

50  54 

1  53  54 

1  57  06 

2  00  32 

—76 

-  96 

8  15 

1  42  58 

45  39 

1  48  30 

1  51  32 

1  54  47 

-72 

-  91 

8  30 

1  37  26 

39  57 

1  42  39 

1  45  31 

1  48  35 

-68 

-  86 

8  45 

1  31  30 

33  51 

1  36  23 

1  39  05 

1  41  57 

—64 

-  80 

9  00 

1  25  12 

27  24 

1  29  44 

1  32  14 

1  34  55 

—59 

-  75 

9  15 

1  18  34 

1  20  36 

1  22  45 

1  25  03 

1  27  30 

-55 

-  69 

9  30 

1  11  37 

1  13  28 

1  15  25 

1  17  31 

1  19  45 

-50 

—  63 

9  45 

1  04  23 

1  06  03 

1  07  48 

1  09  41 

1  11  41 

—45 

-  56 

10  00 

0  56  54 

0  58  22 

0  59  55 

1  01  34 

1  03  20 

-40 

-  50 

10  15 

0  49  12 

0  50  27 

0  51  48 

0  53  14 

0  54  45 

-34 

-  43 

10  30 

0  41  18 

0  42  21 

0  43  28 

0  44  40 

0  45  57 

—29 

—  36 

10  45 

0  33  14 

0  34  05 

0  34  59 

0  35  57 

0  36  59 

—23 

-  29 

11  00 

0  25  02 

0  25  41 

0  26  21 

0  27  05 

0  27  51 

—18 

-  22 

11  15 

0  16  45 

0  17  10 

0  17  38 

0  18  07 

0  18  38 

-12 

—  14 

11  30 

0  08  23 

0  08  36 

0  08  50 

0  09  04 

0  09  20 

-  6 

—  7 

11  45 

2  12  21 

2  15  54 

2  19  40 

2  23  43 

2  28  02 

-93 

—120 

h.  TO.   8. 

h.  TO.   8. 

h.  TO.  8. 

h.  m.  s. 

h.  TO.   8. 

8. 

8. 

5  52  41 

5  52  24 

5  52  06 

5  51  47 

5  51  27 

+  5 

+  7 

46061—08- 


34  GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  4. — Azimuth  and  apparent  altitude  of  Polaris  at  different  hour  angles — Continued. 


Apparent  altitude  of  Polaris,  computed  for  declination  88°  46'  and 

Correc- 

Hour 

mean  refraction. 

tion 

Hour 

angle 

forl' 

angle 

oefore 

in- 

before 

or  after 

crease 

or  after 

upper 
culmi- 
nation. 

Latitude 
30°. 

Latitude 
35°. 

Latitude 
40°. 

Latitude 
45°. 

Latitude 
50°. 

Latitude 
55°. 

Latitude 
60°. 

in  dec- 
i  nation 
of  Po- 

upper 
culmi- 
nation. 

laris. 

h.  m. 

/ 

h.   m. 

000 

31  15.6 

36  15.3 

41  15.1 

46  14.9 

51  14.8 

56  14.6 

61  14.5 

—1.0 

000 

015 

31  15.4 

36  15.2 

41  14.9 

46  14.8 

51  14.6 

56  14.4 

61  14.3 

-1.0 

015 

030 

31  14.9 

36  14.7 

41  14.5 

46  14.3 

51  14.2 

56  14.0 

61  "13.8 

—1.0 

030 

045| 

31  14.2 

36  13.9 

41  13.7 

46  13.5 

51  13.3 

56  13.2 

61  13.0 

-1.0 

045 

100 

31  13.0 

35  12.8 

41  12.5 

46  12.3 

51  12.2 

56  12.0 

61  11.9 

-1.0 

100 

115 

31  11.6 

36  11.3 

41  11.1 

46  10.9 

51  10.8 

56  10.6 

61  10.4 

—0.9 

1  15 

130 

31  09.9 

36  09.6 

41  09.4 

46  09.2 

51  09.0 

56  08.8 

61  08.6 

—0.9 

130 

145 

31  07.9 

36  07.6 

41  07.3 

46  07.2 

51  07.0 

56  06.8 

61  06.6 

—0.9 

145 

200 

31  05.6 

36  05.3 

41  05.0 

46  04.8 

51  04.6 

56  04.4 

61  04.2 

—0.8 

200 

215 

31  03.0 

36  02.7 

41  02.4 

46  02.2 

51  02.0 

56  01.8 

61  01.6 

-0.8 

215 

230 

31  00.1 

35  59.8 

40  59.5 

45  59.3 

50  59.1 

55  58.9 

60  58.7 

-0.8 

230 

245 

30  57.0 

35  56.7 

40  56.5 

45  56.2 

50  56.0 

55  55.8 

60  55.5 

-0.7 

245 

300 

30  53.7 

35  53.4 

40  53.1 

45  52.9 

50  52.6 

55  52.3 

60  52.1 

-0.7 

300 

315 

30  50.1 

35  49.8 

40  49.5 

45  49.2 

50  49.0 

55  48.8 

60  48.5 

—0.6 

315 

330 

30  46.4 

35  46.0 

40  45.7 

45  45.5 

50  45.2 

55  45.0 

60  44.7 

—0.6 

330 

345 

30  42.4 

35  42.1 

40  41.8 

45  41.5 

50  41.3 

55  41.0 

60  40.7 

—0.5 

345 

400 

30  38.3 

35  38.0 

40  37.6 

45  37.4 

50  37.1 

55  36.8 

60  36.5 

—0.5 

400 

415 

30  34.0 

35  33.6 

40  33.3 

45  33.0 

50  32.8 

55  32.5 

60  32.1 

-0.4 

415 

430 

30  29.6 

35  29.2 

40  28.9 

45  28.5 

50  28.3 

55  28.0 

60  27.6 

-0.4 

430 

445 

30  25.0 

35  24.6 

40  24.3 

45  24.0 

50  23.7 

55  23.4 

60  23.0 

-0.3 

445 

500 

30  20.4 

35  20.0 

40  19.7 

45  19.4 

50  19.1 

55  18.8 

60  18.4 

-0.2 

500 

515 

30  15.6 

35  15.3 

40  14.9 

45  14.6 

50  14.3 

55  14.0 

60  13.6 

-0.2 

515 

530 

30  10.8    35  10.4 

40  10.1 

45  09.9 

50  09.6 

55  09.2 

60  08.8 

—0.1 

530 

545 

30  06.0 

35  05.6 

40  05.3 

45  05.0 

50  04.7 

55  04.4 

60  04.0 

0.0 

545 

600 

30  01.2 

35  00.8 

40  00.5 

45  00.2 

49  59.9 

54  59.5 

59  59.1 

0.0 

600 

615 

29  56.4 

34  56.0 

39  55.6 

44  55.3 

49  55.0 

54  54.7 

59  54.3 

+0.1 

615 

630 

29  51.6 

34  51.2 

39  50.8 

44  50.5 

49  50.2 

54  49.9 

59  49.6 

+0.1 

630 

645 

29  46.8 

34  46.4 

39  46.0 

44  45.7 

49  45.5 

54  45.1 

59  44.8 

+0.2 

645 

700 

39  42.1 

34  41.7 

39  41.4 

44  41.1 

49  40.8 

54  40.4 

59  40.1 

+0.3 

700 

715 

29  37.5 

34  37.1 

39  36.8 

44  36.4 

49  36.2 

54  35.8 

59  35.4 

+  0.4 

715 

730 

29  33.0 

34  32.6 

39  32.3 

44  32.0 

49  31.7 

54  31.4 

59  31.0 

+0.4 

730 

745 

29  28.6 

34  28.2 

39  27.9 

44  27.6 

49  27.3 

54  27.0 

59  26.7 

+0.5 

745 

800 

29  24.4 

34  24.0 

39  23.7 

44  23.4 

49  23.1 

54  22.8 

59  22.5 

+0.5 

800 

815 

29  20.3 

34  19.9 

39  19.6 

44  19.3 

49  19.0 

54  18.8 

59  18.4 

+0.6 

815 

830 

29  16.4 

34  16.0 

39  15.7 

44  15.4 

49  15.2 

54  14.9 

59  14.6 

+0.6 

830 

845 

29  12.7 

34  12.3 

39  12.0 

44  11.7 

49  11.5 

54  11.2 

59  11.0 

+0.7 

845 

900 

29  09.2 

34  08.8 

39  08.5 

44  08.3 

49  08.1 

54'  07.9 

59  07.6 

+0.7 

900 

915 

29  05.9 

34  05.5 

39  05.3 

44  05.0 

49  04.8 

54  04.5 

59  04.3 

+0.8 

915 

930 

29  02.8 

34  02.5 

39  02.2 

44  02.0 

49  01.8 

54  01.5 

59  01.3 

+0.8 

930 

945 

29  00.0 

33  59.7 

38  59.4 

43  59.2 

48  59.0 

53  58.8 

58  58.6 

+0.8 

945 

1000 

28  57.5 

33  57.2 

38  56.9 

43  56.7 

48  56.6 

53  56.4 

58  56.1 

+0.9 

1000 

1015 

28  55.3 

33  55.0 

38  54.7 

43  54.5 

48  54.3 

53  54.1 

58  53.9 

+0.9 

1015 

1030 

28  53.3 

33  53.0 

38  52.8 

43  52.5 

48  52.4 

53  52.1 

58  52.0 

+0.9 

1030 

1045 

28  51.6 

33  51.3 

38  51.1 

43  50.8 

48  50.7 

53  50.5 

58  50.3 

+0.9 

1045 

1100 

28  50.2 

33  49.9 

38  49.7 

43  49.5 

48  49.4 

53  49.1 

58  49.0 

+1.0 

1100 

1115 

28  49.2 

33  48.9 

38  48.6 

43  48.4 

48  48.2 

53  48.0 

58  47.9 

+1.0 

11  15 

1130 

28  48.4 

33  48.1 

38  47.8 

43  47.6 

48  47.5 

53  47.2 

58  47.1 

+1.0 

1130 

1145 

28  47.9 

33  47.6 

38  47.4 

43  47.1 

48  47.0 

53  46.8 

58  46.7 

+1.0 

1145 

1200 

28  47.7 

33  47.4 

38  47.2 

43  47.0 

48  46.8 

53  46.7 

58  46.6 

+1.0 

1200 

GEOGRAPHIC  TABLES  AND  FORMULAS. 


35 


\g               2.908 

8.723 

4O  15 

00 

5 

N 

e 

Z 

.006" 
10' 

2.9H 

8.73+ 

\ 

f> 

-cb 

r 

IE 

•5 

f 

y 

.006" 
'         05' 

TV 

B.9J5 

6.745      m, 

• 

\ 

•0 

IS 

4O°QO' 

h                             \               Z.9I9   J                                             8.755   I 

D15f                                                    10  '                        07  Vs'                      OS'                                                    90°00' 

FIG.  7.— Construction  of  polyconic  projection.    15' of  latitude  and  longitude;  scale  1:48000.    Construc- 
tion lines  (to  be  drawn  in  pencil)  dotted;  final  projection  lines  full. 

EXAMPLE    OF    USE    OF   PROJECTION   TABLES. 

Let  it  be  required  to  construct  a  projection  for  the  area  between  parallels  of  40°  OCK 
and  40°  15'  and  meridians  90°  (XX  and  90°  15X  on  a  scale  of  1:48000  (4,000  feet=l  inch). 
For  this  scale  it  is  customary  to  show  meridians  or  parallels  at  intervals  of  5  minutes, 
though  any  other  desired  interval  may  be  adopted. 

Through  the  center  of  the  paper  (see  diagram,  fig.  7)  draw  two  fine  pencil  lines 
a-b  and  c-d  exactly  perpendicular  to  each  other.  The  vertical  line  will  be  the  meri- 
dian of  90°  07X  30"  and  the  intersection  of  the  horizontal  line  with  the  vertical  line 
will  be  a  point  on  the  parallel  of  40°  07X  30".  From  the  column  headed  "Meridional 
distance"  Table  9,  page  82,  opposite  40°  in  column  " Latitude  of  parallel,"  take 

OF  THE 


36  GEOGEAPHIC  TABLES  AND  FORMULAS. 

the  value  of  a  latitude  interval  of  5X,  which  is  7.588  inches;  lay  off  half  of  this  interval 
or  3.794  inches,  on  the  central  meridian  above  and  below  the  horizontal  line;  these 
distances  will  give  points  e  and/,  on  the  parallels  of  40°  10X  and  40°  05X,  respectively. 
The  distance,  7.588  inches,  laid  off  above  and  below  the  latter  points  will  give  points 
g  and  Ti  for  latitudes  40°  15'  and  40°  OO7.  Through  each  of  these  points  draw  a 
line  parallel  to  the  horizontal  line  and  perpendicular  to  the  vertical  line  first  drawn. 

In  a  similar  manner  lay  off  points  on  the  east  and  west  lines  through  latitude 
points  40°  (h),  and  40°  15X  (g),  by  measuring  from  the  meridian  east  and  west  dis- 
tances obtained  from  the  columns  headed  "Abscissas  of  developed  parallel"  in 
Table  9,  page  82,  for  the  -appropriate  latitude  and  for  the  longitude  intervals  of  2Y 
and  7Y-  Thus,  for  40°,  the  tabular  value  for  2JX  is  2.919  inches,  for  5'  it  is  5.837 
inches,  and  for  1\'  it  is  8.755  inches.  The  points  so  found  (i,  j,  k,  I)  will  be  on  the 
meridians  of  90°  00',  90°  05',  90°  1(K,  and  90°  15'.  Find  similar  points  for  latitude 
40°  157,  and  join  corresponding  points  with  light  pencil  lines.  In  order  to  find  points 
on  these  meridians  where  each  parallel  of  latitude  crosses,  take  from  the  columns 
headed  "Ordinates  of  developed  parallel"  in  Table  9,  on  the  same  page,  opposite 
the  given  latitude  40°,  the  distance  for  the  "Longitude  interval"  2y  and  7J'  (the 
value  of  2y  for  the  1:48000  scale  is  inappreciable,  being  less  than  0.001  inch);  lay 
these  distances  off  northward  along  the  meridian  from  the  horizontal  lines,  giving 
points  x,  y,  z,  etc.,  on  the  desired  parallels,  and  through  these  points  draw  curved 
lines  concave  toward  the  north.  After  testing  the  accuracy  of  the  plotting  by  com- 
paring the  length  of  the  diagonals  /-i=/-Z,  h-m=h-n,  etc.,  the  projection  may  be 
inked  in. 

In  a  similar  manner  projections  may  be  constructed  for  other  scales  or  areas, 
Table  7,  for  the  scale  of  1:63360  (1  mile  to  1  inch),  may  be  used  for  any  even  fraction 
or  multiple  of  a  mile.  The  distance  between  parallels  being  found  from  column 
"Meridional  distance;"  distances  not  given  may  be  found  by  simple  proporticn 
except  for  "ordinates  of  developed  parallel,"  which  increase  as  the  square  of  the 
distance  from  the  central  meridian.  For  scales  of  any  number  of  thousands  of  feet 
to  1  inch,  use  suitable  fractions  of  the  distance  given  for  scale  1:12000  (1,000  feet  to 
1  inch)  in  Table  10. 

For  maps  of  large  areas  Table  5  gives  the  actual  or  full  scale  distances  in  meters. 
These  may  be  divided  by  the  proper  scale  ratio  and  the  distances  so  found  platted  with 
a  metric  scale  or  reduced  to  feet  by  the  table  on  page  268;  the  X  values  are  the  dis- 
tances from  the  central  horizontal  line  measured  to  the  north  or  south,  and  the 
corresponding  Y  values  give  the  offsets  northward  to  points  on  the  curved  parallels. 
The  distances  measured  east  and  west  from  the  central  meridian  are  those  in  the 
part  of  Table  5  entitled  "Arcs  of  the  parallel"  (p.  39),  each  to  be  taken  for  the 
proper  latitude.  For  projections  of  large  extent  the  meridians  differ  sensibly  from 
straight  lines  and  they  as  well  as  the  parallels  must  be  drawn  as  curves. 


GEOGRAPHIC  TABLES  AMD  FORMULAS. 


37 


TABLE  5. — For  projection  of  maps  of  large  areas. 

[The  ratio  of  the  yard  to  the  meter  as  stated  by  Clarke,  namely,  1  meter  =  1.093623  yards  =  39.370432 
inches,  is  that  used  in  the  table.] 

LENGTHS  OF  DEGREES  OF  THE  MERIDIAN. 


Latitude. 

Meters.  « 

Statute 
miles. 

Latitude. 

Meters.  « 

Statute 
miles. 

0 

o 

0 

110,  567.  2 

68.  704 

45 

111,  130.  9 

69.  054 

1 

110,  567.  6 

68.704 

46 

111,  150.  6 

69.  066 

2 

110,  568.  6 

68.  705 

47 

111,170.4 

69.  079 

3 

110,570.3 

68.  706 

48 

111,190.1 

69.  091 

4 

110,  572.  7 

68.  708 

49 

111,  209.  7 

69.  103 

5 

110,  575.  8 

68.  710 

50 

111,  229.  3 

69.  115 

6 

110,579.5 

68.  712 

51 

111,248.7 

69.  127 

7 

110,  583.  9 

68.  715 

52 

111,268.0 

69.  139 

8 

110,  589.  0 

68.  718 

53 

111,  287.  1 

69.  151 

9 

110,  594.  7 

68.  721 

54 

111,306.0 

69.  163 

10 

110,  601.  1 

68.  725 

55 

111,  324.  8 

69.  175 

11 

110,608.1 

68.  730 

56 

111,  343.  3 

69.  186 

12 

110,615.8 

68.  734 

57 

111,361.5 

69.  197 

13 

110,  624.  1 

68.  739 

58 

111,379.5 

69.  209 

14 

110,  633.  0 

68.  744 

59 

111,397.2 

69.  220 

15 

110,  642.  5 

68.  751 

60 

111,  414.  5 

69.  230 

16 

110,  652.  6 

68.  757 

61 

111,431.5 

69.  241 

17 

110,  663.  3 

68.764 

62 

111,448.2 

69.  251 

18 

110,674.5 

68.  771 

63 

111,464.4 

69.  261 

19 

110,686.3 

68.  778 

64 

111,480.3 

69.  271 

20 

110,698.7 

68.  786 

65 

111,  495.  7 

69.  281 

21 

110,711.6 

68.  794 

66 

111,510.7 

69.  290 

22 

110,725.0 

68.  802 

67 

111,525.3 

69.  299 

23 

110,  738.  8 

68.  811 

68 

111,539.3 

69.  308 

24 

110,  753.  2 

68.  820 

69 

111,  552.  9 

69.  316 

25 

110,  768.  0 

68.829 

70 

111,  565.  9 

69.  324 

26 

110,  783.  3 

68.  839 

71 

111,578.4 

69.  332 

27 

110,  799.  0 

68.  848 

72 

111,  590.  4 

69.  340 

28 

110,  815.  1 

68.  858 

73 

111,  601.  8 

69.  347 

29 

110,  831.  6 

68.  869 

74 

111,612.7 

69.  354 

30 

110/848.  5 

68.  879 

75 

111,622.9 

69.  360 

31 

110,  865.  7 

68.  890 

76 

111,  632.  6 

69.  366 

32 

110,  883.  2 

68.  901 

77 

111,  641.  6 

69.  372 

33 

110,  901.  1 

68.  912 

78 

111,  650.  0 

69.  377 

34 

110,  919.  2 

68.  923 

79 

111,  657.  8 

69.  382 

35 

110,  937.  6 

68.  935 

80 

111,  664.  9 

69.  386 

36 

110,956.2 

68.  946 

81 

111,671.4 

69.  390 

37 

110,  975.  1 

68.  958 

82 

111,  677.  2 

69.  394 

38 

110,  994.  1 

68.  969 

83 

111,  682.  4 

69.  397 

39 

111,013.3 

68.  981 

84 

111,  686.  9 

69.400 

40 

111,  032.  7 

68.  993 

85 

111,  690.  7 

69.  402 

41 

111,  052.  2 

69.  006 

86 

111,  693.  8 

•    69.404 

42 

111,071.7 

69.  018 

87 

111,  696.  2 

69.  405 

43 

111,091.4 

69.  030 

88 

111,  697.  9 

69.  407 

44 

111,111.1 

69.  042 

89 

111,  699.  0 

69.  407 

45 

111,  130.  9 

69.  054 

90 

111,  699.  3 

69.  407 

a  These  quantities  express  the  number  of  meters  and  statute  miles  contained  within  an  arc  of  which 
the  degree  of  latitude  named  is  the  middle;  thus,  the  quantity  111,032.7,  opposite  latitude  40°,  is  the 

38 


GEOGRAPHIC   TABLES    AND   FORMULAS. 


TABLE  5. — For  projection  of  maps  of  large  areas — Continued. 

[Extracted  from  Appendix  No.  6,  U.  S.  Coast  and  Geodetic  Survey  Report  for  1884.] 

LENGTHS  OF  DEGREES  OF  THE  PARALLEL. 


Latitude. 

Meters. 

Statute 
miles. 

Latitude. 

Meters. 

Statute 
miles. 

o 

o 

0 

111,321 

69.  172 

45 

78,  849 

48.  995 

1 

111,  304 

69.  162 

46 

77,466 

48.  136 

2 

111,253 

69.  130 

47 

76,  058 

47.  261 

3 

111,  169 

69.  078 

48 

74,  628 

46.  372 

4 

111,051 

69.  005 

49 

73,  174 

45.  469 

5 

110,900 

68.  911 

50 

71,  698 

44.  552 

6 

110,  715 

68.  795 

51 

70,  200 

43.  621 

7 

110,497 

68.  660 

52 

68,  680 

42.  676 

8 

110,245 

68.  504 

53 

67,  140 

41.719 

9 

109,  959 

68.  326 

54 

65,  578 

40.  749 

10 

109,641 

68.129 

55 

63,  996 

39.  766 

11 

109,  289 

67.  910 

56 

62,  395 

38.  771 

12 

108,  904 

67.  670 

57 

60,  774 

37.  764 

13 

108,  486 

67.  410 

58 

59,  135 

36.  745 

14 

108,  036 

67.  131 

59 

57,  478 

35.  716 

15 

107,  553 

66.  830 

60 

55,  802 

34.  674 

16 

107,  036 

66.  510 

61 

54,110 

33.  623 

17 

106,  487 

66.  169 

62 

52,400 

32.  560 

18 

105,  906 

65.  808 

63 

50,  675 

31.488 

19 

105,  294 

65.  427 

64 

48,934 

30.  406 

20 

104,649 

65.  026 

65 

47,  177 

29.  315 

21 

103,  972 

64.606 

66 

45,  407 

28.  215 

22 

103,  264 

64.  166 

67 

43,  622 

27.  106 

23 

102,  524 

63.  706 

68 

41,  823 

25.  988 

24 

101,754 

63.  228 

69 

40,  012 

24.  862 

25 

100,  952 

62.  729 

70 

38,  188 

23.  729 

26 

100,  119 

62.  212 

71 

36,  353 

22.  589 

27 

99,  257 

61.  676 

72 

34,  506 

21.  441 

28 

98,  364 

61.  122 

73 

32,648 

20.  287 

29 

97,441 

60.  548 

74 

30,  781 

19.  127 

30 

96,  488 

59.  956 

75 

28,  903 

17.  960 

31 

95,  506 

59.  345 

76 

27,  017 

16.  788 

32 

94,  495 

58.  716 

77 

25,123 

15.  611 

33 

93,  455 

58.  071 

78 

23,  220 

14.  428 

34 

92,  387 

57.  407 

79 

21,  311 

13.  242 

35 

91,  290 

56.  725 

80 

19,  394 

12.  051 

36 

90,  166 

56.  027 

81 

17,  472 

10.  857 

37 

89,  014 

55.  311 

82 

15,  545 

9.659 

38 

87,  835 

54.  579 

83 

13,  612 

8.458 

39 

86,  629 

53.  829 

84 

11,675 

7.255 

40 

85,  396 

53.063 

85 

9,735 

6.049 

41 

84,  137 

52.  281 

86 

7,792 

4.842 

42 

82,  853 

51.  483 

87 

5,846 

3.632 

43 

81,543 

50.  669 

88 

3,898 

2.422 

44 

80,  208 

49.  840 

89 

1,949 

1.211 

45 

78,  849 

48.  995 

90 

0 

0.000 

GEOGRAPHIC    TABLES    AND   FOKMULAS. 


39 


TABLE  5. — For  projection  of  maps  of  large  areas — Continued. 

[Extracted  from  Appendix  No.  6,  U.  S.  Coast  and  Geodetic  Survey  Report  for  1884.] 

ARCS  OF  THE  PARALLEL  IN  METERS. 


Latitude. 

Value  of  1'. 

Latitude. 

Value  of  1'. 

Latitude. 

Value  of  1'. 

0      / 

o    / 

O     f 

24  00 

1695.  9 

33  00 

1557.  6 

42  00 

1380.  9 

10 

1693.  7 

10 

1554.  7 

10 

1377.  3 

20 

1691.5 

20 

1551.  7 

20 

1373.  7 

30 

1689.  3 

30 

1548.  7 

30 

1370.  0 

40 

1687.  0 

40 

1545.  8 

40 

1366.  4 

50 

1684.  8 

50 

1542.  8 

50 

1362.  7 

25  00 

1682.  5 

34  00 

1539.  8 

43  00 

1359.  1 

10 

1680.  3 

10 

1536.  8 

10 

1355.  4 

20 

1678.  0 

20 

1533.  7 

20 

1351.  7 

30 

1675.  7 

30 

1530.  7 

30 

1348.  0 

40 

1673.  3 

40 

1527.  6 

40 

1344.  3 

50 

1671.0 

50 

1524.  6 

50 

1340.  5 

26  00 

1668.  7 

35  00 

1521.  5 

44  00 

1336.  8 

10 

1666.  3 

10 

1518.  4 

10 

1333.  1 

20 

1663.  9 

20 

1515.  3 

20 

1329.  3 

30 

1661.  5 

30 

1512.  2 

30 

1325.  5 

40 

1659.  1 

40 

1509.  1 

40 

1321.  7 

50 

1656.  7 

50 

1505.  9 

50 

1318.0 

27  00 

1654.3 

36  00 

1502.  8 

45  00 

1314.  2 

10 

1651.  8 

10 

1499.  6 

10 

1310.  3 

20 

1649.  4 

20 

1496.4 

20 

1306.  5 

30 

1646.  9 

30 

1493.  2 

30 

1302.  7 

40 

1644.4 

40 

1490.0 

40 

1298.  8 

50 

1641.9 

50 

1486.  8 

50 

1295.0 

28  00 

1639.  4 

37  00 

1483.  6 

46  00 

1291.0 

10 

1636.9 

10 

1480.  3 

10 

1287.  2 

20 

1634.  3 

20 

1477.  1 

20 

1283.  3 

30 

1631.8 

30 

1473.  8 

30 

1279.  4 

40 

1629.  2 

40 

1470.  5 

40 

1275.  5 

50 

1626.  6 

50 

1467.  2 

50 

1271.6 

29  00 

1624.  0 

38  00 

1463.  9 

47  00 

1267.  6 

10 

1621.4 

10 

1460.  6 

10 

1263.  7 

20 

1618.  8 

20 

1457.  3 

20 

1259.  7 

30 

1616.  1 

30 

1453.  9 

30 

1255.  8 

40 

1613.5 

40 

1450.  6 

40 

1251.  8 

50 

1610.8 

50 

1447.  2 

.   50 

1247.  8 

30  00 

1608.  1 

39  00 

1443.  8 

48  00 

1243.  8 

10 

1605.  4 

10 

1440.  4 

10 

1239.  8 

20 

1602.  7 

20 

1437.  0 

20 

1235.  8 

30 

1600.  0 

30 

1433.  6 

30 

1231.  7 

40 

1597.  3 

40 

1430.  2 

40 

1227.  7 

50 

1594.  5 

50 

1426.  7 

50 

1223.  6 

31  00 

1591.  8 

40  00 

1423.  3 

49  00 

1219.  6 

10 

1589.  0 

10 

1419.8 

10 

1215.5 

20 

1586.  2 

20 

1416.  3 

20 

1211.4 

30 

1583.  4 

30 

1412.  8 

30 

1207.  3 

40 

1580.  6 

40 

1409.  3 

40 

1203.  2 

50 

1577.  8 

50 

1405.  8 

50 

1199.  1 

32  00 

1574.  9 

41  00 

1402.  3 

50  00 

1195.  0 

10 

1572.  1 

10 

1398.  8 

10 

1190.  8 

20 

1569.  2 

20 

1395.  2 

20 

1186.  7 

30 

1566.  3 

30 

1391.  6 

30 

1182.  5 

40 

1563.4 

40 

1388.  1 

40 

1178.  4 

50 

1560.5 

50 

1384.  5 

50 

1174.  2 

40 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.  —  Values  of  X  and  Y  in  meters. 

Latitude  24°. 

Latitude  25°. 

Latitude  26°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

o     / 

0        / 

0       1 

1   00 

101,753 

361 

1    00 

100,  951 

372 

1   00 

100,118 

383 

2   00 

203,500 

1,445 

2   00 

201,896 

1,489 

2   00 

200,  231 

1,532 

3   00 

305,  237 

3,250 

3   00 

302,831 

3,351 

3   00 

300,  332 

3,447 

4   00 

406,  959 

5,778 

4   00 

403,  749 

5,957 

4  00 

400,416 

6,128 

6   00 

508,660 

9,028 

5   00 

504,645 

9,307 

5   00 

500.476 

9,574 

6   00 

610,  336 

13,001 

6   00 

605,  514 

13,  401 

6   00 

600,506 

13,  786 

7   00 

711,  981 

17,  695 

7   00 

706,  349 

18,  239 

7   00 

700,501 

18,  763 

8  00 

813,590 

23,109 

8   00 

807,  146 

23,821 

8   00 

800,456 

24,  505 

9  00 

915,  159 

29,245 

9   00 

907,  899 

30,146 

9   00 

900,364 

31,011 

10  00 

1.  016,  681 

36,  102 

10   00 

1,008,603 

37,  215 

10   00 

,  000,  218 

38,  282 

11   00 

1,118,152 

43,679 

11   00 

1,109,252 

45,026 

11   00 

,100,015 

46,  316 

12   00 

1,219,566 

51,  977 

12   00 

1,209,841 

53,  578 

12  00 

,  199,  747 

55,114 

13   00 

1,320,919 

60,994 

13  oe 

1,310,364 

62,873 

13   00 

,299,409 

64,675 

14   00 

1,  422,  205 

70,  731 

14   00 

1,410,815 

72,909 

14  00 

,  398,  994 

74,998 

15   00 

1,523,420 

81,186 

15   00 

1,511,190 

83,  685 

15   00 

,498,498 

86,  082 

16   00 

1,624,558 

92,360 

16   00 

1,611,483 

95,202 

16  00 

,  597,  914 

97,928 

17   00 

1,725,614 

104,  251 

17   00 

1,711,688 

107,  458 

17   00 

,  697,  237 

110,534 

18   00 

1,  826,  583 

116,  859 

18   00 

1,811,800 

120,  453 

18  00 

,  796,  460 

123,  899 

19   00 

1,  927,  460 

130,184 

19   00 

1,911,813 

134,  186 

19   00 

,  895,  578 

138,023 

20   00 

2,028,240 

144,  225 

20   00 

2,011,722 

148,  656 

20   00 

1,994,585 

152,905 

21   00 

2,  128,  918 

158,  981 

21   00 

2,  111,  522 

163,  862 

21   00 

2,  093,  475 

168,  544 

22   00 

2,229,488 

174,  451 

22   00 

2,211,207 

179,805 

22  00 

2,192,243 

184,  939 

23   00 

2,329,946 

190,  634 

23   00 

2,  310,  771 

196,  482 

23   00 

2,  290,  882 

202,  089 

24   00 

2,430,287 

207,530 

24   00 

2,410,210 

213,  894 

24   00 

2,  389,  387 

219,  993 

25   00 

2,  530,  505 

225,  1S8 

25   00 

2,509,518 

232,  038 

25  00 

2,487,753 

238,650 

26   00 

2,  630,  596 

243,458 

26   00 

2,  608,  689 

250,  914 

26   00 

2,  585,  973 

258,  061 

27   00 

2,730,554 

262,487 

27   00 

2,  707,  718 

270,  521 

27   00 

2,684,042 

278,  222 

28   00 

2,  830,  374 

282,  225 

28   00 

2,  806,  600 

290,859 

28  00 

2,781,953 

299,  132 

29   00 

2,  930,  052 

302,  671 

29   00 

2,905,329 

311,925 

29   00 

2,879,702 

320,788 

30   00 

3,029,582 

323,825 

30   00 

3,003,900 

333,718 

30   00 

2,  977,  281 

343,  197 

GEOGRAPHIC   TABLES    AND    FORMULAS. 


41 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.  —  Values  of  X  and  Y  in  meters. 

Latitude  27°. 

Latitude  28°. 

Latitude  29°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

o      / 

o      / 

o      / 

1  00 

99,256 

393 

1   00 

98,  363 

403 

1   00 

97,439 

412 

2  00 

198,505 

1,573 

2   00 

196,  719 

1,612 

2   00 

194,872 

1,649 

3   00 

297,  742 

3,539 

3   00 

295,062 

3,627 

3   00 

292,  291 

3,710 

4   00 

396,960 

6,291 

4   00 

393,385 

6,447 

4   00 

389,689 

6,595 

5  00 

4%,  154 

9,829 

5  00 

491  ,  682 

10,073 

5   00 

487,  059 

10,  305 

6   00 

595,  316 

14,154 

6   00 

589,  945 

14,505 

6   00 

584,394 

14,  838 

7   00 

694,  440 

19,264 

7   00 

688,168 

19,  741 

7   00 

681,687 

20,  194 

8   00 

79S,  522 

25,159 

8  00 

786,  347 

25,  782 

8   00 

778,931 

26,374 

9   00 

892,554 

31,839 

9   00 

884,472 

32,  627 

9   00 

876,  120 

33,376 

10   00 

991,529 

39,303 

10   00 

982,  537 

40,276 

10   00 

973,  246 

41,  199 

11   00 

1,090,442 

47,551 

11   00 

1,080,537 

48,  728 

11   00 

1,070,302 

49,845 

12   00 

1,189,287 

56,583 

12   00 

,178,464 

57,983 

12   00 

1,167,282 

59,  313 

13   00 

1,288,057 

66,398 

13   00 

1,  276,  312 

68,040 

13   00 

1,264,178 

69,  601 

14  00 

1,  386,  746 

76,995 

14   00 

,374,075 

78,899 

14   00 

1,360,983 

80,706 

15   00 

1,485,348 

88,374 

15   00 

,  471,  745 

90,558 

15   00 

1,457,691 

92,  631 

16   00 

1,583,857 

100,534 

16   00 

,569,315 

103,  017 

16   00 

1,554,295 

105,  375 

17   00 

1,682,267 

113,  474 

17   00 

,  666,  781 

116,2/5 

17  00 

1,650,787 

118,  935 

18   00 

1,780,570 

127,  193 

18   00 

,  764,  135 

130,331 

18   00 

1,747,161 

133,311 

19  00 

1,878,762 

141,690 

19   00 

1,861,371 

145,  185 

19   00 

1,843,410 

148,602 

20  00 

1,976,836 

156,966 

20   00 

1,958,481 

160,835 

20  00 

1,939,527 

164,506 

21   00 

2,  074,  786 

173,  018 

21   00 

2,055,460 

177.280 

21   00 

2,035,505 

181,324 

22  00 

2,  172,  606 

189,  845 

22   00 

2,  152,  302 

194,518 

22   00 

2,  131,  338 

198,  953 

23   00 

2,  270,  289 

207,447 

23   00 

2,248,998 

212,550 

23   00 

2,  227,  020 

217,  392 

24   00 

2,  367,  830 

225,823 

24   00 

2,345,544 

231,  374 

24   00 

2,322,539 

236,640 

25   00 

2,465,222 

244,  970 

25  00 

2,441,932 

250,  988 

25  00 

2,417,893 

256,  695 

26   00 

2,  562,  459 

264,889 

26   00 

2,538,156 

271,  391 

26   00 

2,  513,  074 

277,558 

27   00 

2,  659,  535 

285,577 

27   00 

2,634,210 

292,  &82 

27   00 

2,608,075 

299,  224 

28   00 

2,756,445 

307,035 

28   00 

2,  730,  087 

314,  559 

28  00 

2,702,890 

321,  694 

29  00 

2,853,181 

329,  259 

29   00 

2,  825,  779 

337,321 

29   00 

2,797,511 

344,  964 

80  00 

2,  949,  739 

352,249 

30   00 

2,921,284 

360,866 

30  00 

2,891,931 

369,  036 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.  —  Values  of  X  and  Y  in  meters. 

Latitude  30°. 

Latitude  31°. 

Latitude  32°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

o     / 
1  00 

96,  487 

421 

0       / 

1   00 

95,505 

429 

o     / 
1  00 

94,  494 

437 

2   00 

192,  967 

1,684 

2   00 

191,  002 

1,717 

2   00 

188,980 

1,748 

3   00 

289,  432 

3,789 

3   00 

286,484 

3,863 

3   00 

283,  449 

3,933 

4   00 

385,  875 

6,735 

4   00 

381,943 

6,867 

4   00 

377,  894 

6,991 

5   00 

482,  288 

10,  523 

5   00 

477,371 

10,  729 

5   00 

472,  307 

10,922 

6   00 

578,665 

15,  153 

6   00 

572,  760 

15,  450 

6   00 

566,  680 

15,  727 

7   00 

674,  998 

20,  623 

7   00 

668,  103 

21,  027 

7   00 

661,  004 

21,  404 

8   00 

771,279 

26,934 

8   00 

763,  392 

27,  461 

8   00 

755,  272 

27,  954 

9  00 

867,  502 

34,084 

9   00 

858,619 

34,751 

9   00 

849,  475 

35,  375 

10   00 

963,658 

42,  074 

10   00 

953,  777 

42,  897 

10   00 

943,  605 

43,  667 

11   00 

1,059,741 

50,903 

11   00 

1,048,858 

51,898 

11   00 

1,  037,  655 

52,  829 

12   00 

1,155,744 

60,  570 

12   00 

1,  143,  854 

61,  753 

12   00 

1,131,616 

62,  861 

13   00 

1,  251,  658 

71,074 

13   00 

1,238,758 

72,462 

13   00 

1,  225,  480 

73,  761 

14   00 

1,347,477 

82,  415 

14   00 

1,  333,  561 

84,024 

14  00 

1,319,239 

85,  529 

15   00 

1,  443,  193 

94,  591 

15   00 

1,  428,  257 

96,  437 

15  00 

1,412,885 

98,  164 

16   00 

1,  538,  800 

107,  603 

16.00 

1,522,837 

109,  701 

16   00 

1,506,411 

111,664 

17   00 

1,  634,  290 

121,449 

17   00 

1,  617,  294 

123,  815 

17   00 

1,599,808 

126,  029 

18   00 

1,  729,  654 

136,  127 

18   00 

1,711,621 

138,777 

18   00 

1,  693,  067 

141,  256 

19   00 

1,  824,  887 

151,637 

19   00 

1,  805,  810 

154,586 

19   00 

1,  786,  182 

157,346 

20   00 

1,  919,  982 

167,  977 

20   00 

1,899,852 

171,  241 

20   00 

1,  879,  144 

174,  296 

21   00 

2,014,930 

185,  147 

21   00 

1,  993,  740 

188,  741 

21   00 

1,971,946 

192,  105 

22   00 

2,  109,  725 

203,  143 

22   00 

2,  087,  468 

207,  085 

22   00 

2,064,579 

210,  772 

23   00 

2,204,359 

221,966 

23  00 

2,  181,  027 

226,  270 

23   00 

2,  157,  035 

230,  295 

24   00 

2,  298,  825 

241,  616 

24   00 

2,274,411 

246,295 

24   00 

2,  249,  305 

250,  672 

25   00 

2,  393,  116 

262,  089 

25   00 

2,  367,  610 

267,  159 

25   00 

2,  341,  385 

271,  901 

26   00 

2,  487,  224 

283,383 

26   00 

2,460,618 

288,860 

26   00 

2,  433,  264 

293,  981 

27   00 

2,  581,  144 

305,  498 

27   00 

2,  553,  427 

311,396 

27   00 

2,524,935 

316,  910 

28   00 

2,  674,  867 

328,  432 

28   00 

2,  646,  029 

334,  765 

28   00 

2,  616,  390 

340,  686 

29   00 

2,768,385 

352,  183 

29   00 

2,  738,  418 

358,966 

29   00 

2,  707,  621 

365,  307 

30   00 

2,861,694 

376,  749 

30   00 

2,830,585 

383,  997 

30   00 

2,  798,  621 

390,  770 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


43 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 

COORDINATES  OF  CURVATURE. 


Natural  scale.—  Values  of  X  and  Y  in  meters. 

Latitude  33°. 

Latitude  34°. 

Latitude  35°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

o     / 

o     / 

o     / 

1   00 

93,454 

444 

1   00 

92,385 

451 

1  00 

91,289 

457 

2   00 

186;  899 

1,777 

2   00 

184,  762 

1,803 

2   00 

182,  568 

1,828 

3  00 

280,328 

3,997 

3   00 

277,  121 

4,057 

3   00 

273,  830 

4,112 

4  00 

373,731 

7,106 

4   00 

369,454 

7,212 

4   00 

365,064 

7,310 

5  00 

467,100 

11,102 

5  00 

461,751 

11,268 

5   00 

456,  261 

11-,  421 

6   00 

560,428 

15,986 

6  00 

554,004 

16,  225 

6   00 

547,  412 

16,  445 

7   00 

653,704 

21,  757 

7   00 

646,205 

22,  082 

7   00 

638,509 

22,  381 

8   00 

746,922 

28,  414 

8  00 

738,344 

28,839 

8   00 

729,  542 

29,  229 

9   00 

840,  072 

35,  957 

9   00 

830,  413 

36,  494 

9  00 

820,501 

36,  987 

10  00 

933,  146 

44,385 

10  00 

922,403 

45,  048 

10   00 

911,379 

45,  656 

11   00 

1,026,136 

53,  697 

11   00 

1,  014,  305 

54,499 

11   00 

1,002,165 

55,234 

12   00 

1.1W.033 

63,893 

12   00 

1,106,110 

64,846 

12   00 

1,092,850 

65,721 

13   00 

1,211,829 

74,  971 

13   00 

1,  197,  809 

•  76,089 

13  00 

1,  183,  426 

77,115 

14  00 

1,304,515 

86,931 

14  00 

1,289,395 

88,227 

14  00 

1,273,884 

89,  415 

15  00 

1,397,083 

99,  771 

15  00 

1,380,858 

101,258 

15  00 

1,364,214 

102,  619 

16  00 

1,489,526 

113,491 

16   00 

1,472,190 

115,180 

16   00 

1,454,407 

116,  728 

17   00 

1,581,834 

128,  089 

17   00 

1,563,381 

129,  993 

17   00 

1,544,454 

131,738 

18  00 

1,673,998 

143,564 

18   00 

1,654,423 

145,  696 

18  00 

1,634,347 

147,  650 

19  00 

1,  766,  Oil 

159,  914 

19   00 

1,  745,  308 

162,  287 

19   00 

1,724,076 

164,  460 

20  00 

1,857,866 

177,  138 

20  00 

1,836,026 

179,763 

20   00 

1,813,632 

182,  168 

21   00 

1,949,553 

195,234 

21   00 

1,926,569 

198,  124 

21   00 

1,903,006 

200,  772 

22  00 

2,041,062 

214,201 

22   00 

2,016,929 

217,  368 

22   00 

1,992,190 

220,  268 

23   00 

2,  132,  387 

234,  037 

23  00 

2,  107,  097 

237,  493 

23  00 

2,081,174 

240.  657 

24   00 

2,223,521 

254,  740 

24   00 

2,  197,  065 

258,  497 

24  00 

2,  169,  949 

261,936 

25   00 

2,314,453 

276,309 

25  00 

2,286,823 

230,378 

25  00 

2,  258,  507 

284,  102 

26  00 

2,405,175 

298,  741 

26   00 

2,376,363 

303,  134 

26  00 

2,  346,  838 

307,  154 

27   00 

2,  495,  680 

322,034 

27   00 

2,465,677 

326,  763 

27   00 

2,434,934 

331,089 

28  00 

2,585,961 

346,  187 

28   00 

2,554,756 

351,  262 

28  00 

2,  522,  787 

355,  905 

29   00 

2,676,007 

371,  197 

29   00 

2,  643,  591 

376,  629 

29  OC 

2,  610,  386 

381,598 

30   00 

2,  765,  812 

397,  061 

30   00 

2,  732,  175 

402,  863 

30   00 

2,697,724 

408,  168 

44 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 

COORDINATES  OF  CURVATURE. 


Natural  scale.—  Values  of  X  and  Y  meters. 

Latitude  36°. 

Latitude  37°. 

Latitude  38°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

o     / 

0       / 

o     / 

1    00 

90,164 

462 

1  00 

89,  012 

467 

1   00 

87,  833 

472 

2   00 

180,  319 

1,850 

2   00 

178,  015 

1,870 

2   00 

175,  656 

1.888 

3   00 

270,455 

4,162 

3   00 

266,  997 

4,207 

3   00 

263,458 

4,247 

4   00 

360,  562 

7,399 

4   00 

355,  951 

7,479 

4   00 

351,  230 

7,549 

5  00 

450,  631 

11,  560 

5   00 

444,865 

11,  685 

5  00 

438,962 

11,  795 

6   00 

540,653 

16,  645 

6   00 

533,  730 

16,  824 

6  00 

526,  643 

16,  983 

7   00 

630,  618 

22,652 

7   00 

622,  536 

22,  896 

7   00 

614,  263 

23,112 

8   00 

720,  517 

29,  583 

8   00 

711,273 

29,901 

8  00 

701,812 

30,  183 

9   00 

810,  340 

37,435 

9   00 

799,  932 

37,838 

9   00 

789,  280 

38,195 

10   00 

900,078 

46,  209 

10   00 

888,503 

46,706 

10   00 

876,  657 

47,  145 

11   00 

989,  720 

55,903 

11   00 

976,975 

56,503 

11    00 

963,  933 

57,  034 

12   00 

1,  079,  259 

66,515 

12   00 

1,065,340 

67,  229 

12   00 

1,051,098 

67,860 

13   00 

1,168,684 

78,046 

13   00 

1,153,587 

78,882 

13   00 

1,138,141 

79,622 

14   00 

1,257,987 

90,494 

14   00 

1,241,707 

91,462 

14  00 

1,225,053 

92,  319 

15   00 

1,347,156 

103,  856 

15  00 

1,  329,  690 

104,  967 

15  00 

1,311,823 

105,  949 

16   00 

1,  436,  184 

118,  133 

16   00 

1,  417,  526 

119,  395 

16   00 

1,398,441 

120,511 

17   00 

1,525,061 

133,  323 

17   00 

1,505,206 

134,  745 

17   00 

1,484,899 

136,  002  - 

18   00 

1,  613,  777 

149,  423 

18  00 

1,  592,  721 

151,  015 

18   00 

1,571,185 

152,421 

19   00 

1,702,324 

166,433 

19   00 

1,680,059 

168,203 

19   00 

1,657,289 

169,  767 

20   00 

1,  790,  691 

184,350 

20   00 

1,767,211 

186,  307 

20   00 

1,743,202 

188,037 

21   00 

1,  878,  870 

203,  173 

21   00 

1,  854,  169 

205,  326 

21   00 

1,828,914 

207,229 

22   00 

1,966,851 

222,899 

22   00 

1,940,922 

225,258 

22   00 

1,914,415 

227,  341 

23   00 

2,  054,  625 

243,  527 

23  00 

2,  027,  462 

246,099 

23   00 

1,999,694 

248,  370 

24   00 

2,  142,  183 

265,055 

24   00 

2,113,777 

267,  849 

24  00 

2,084,743 

270,  315 

25   00 

2,229,516 

287,479 

25   00 

2,  199,  860 

290,503 

25   00 

2,169,551 

293,  172 

26   00 

2,316,613 

310,  798 

26   00 

2,  285,  699 

314,  061 

26   00 

2,  254,  109 

316,  939 

27   00 

2,403,467 

335,009 

27   00 

2,371,287 

338,519 

27   00 

2,338,406 

341,  613 

28   00 

2,  490,  068 

360,  111 

28   00 

2,  456,  612 

363,  874 

28   00 

2,  422,  433 

367,  192 

29   00 

2,  576,  407 

386,099 

29   00 

2,541,667 

390,  125 

29   00 

2,  506,  181 

393,  672 

30   00 

2,662,475 

412,  971 

30   00 

2,626,441 

417,  267 

30   00 

2,  589,  639 

421,  050 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


45 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.—  Values  of  X  and  Y  in  meters. 

Latitude  39°. 

Latitude  40°. 

Latitude  41°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

O        1 

O       i 

0       / 

1    00 

86,627 

476 

1   00 

85,394 

479 

1  00 

84,  136 

482 

2   00 

173,  243 

1,903 

2   00 

170,  778 

1,916 

2  00 

168,  260 

1,927 

3   00 

259,  8o9 

4,281 

3   00 

256,  140 

4,311 

3  00 

252,  363 

4,335 

4  00 

346,403 

7,611 

4  00 

341,470 

7,663 

4  00 

336,432 

7,706 

5  00 

432,  925 

11,891 

5  00 

426,  757 

11,972 

5  00 

420,  457 

12,039 

6   00 

519,  396 

17,121 

6   00 

511,990 

17,238 

6   00 

504,428 

17,335 

7   00 

605,803 

23,300 

7   00 

597,  158 

23,460 

7   00 

588,332 

23,  591 

8   00 

692,  138 

30,428 

8   00 

682,  252 

30,  637 

8   00            672,159 

30,807 

9   00 

778,  388 

38,504 

9   00 

767,260 

38,768 

9   00 

755,  897 

38,983 

10   00 

864,545 

47,  527 

10   00 

852,  171 

47,852 

10   00 

839,  537 

48,118 

11   00 

950,  598 

57,496 

11   00 

936,975 

57,888 

11   00 

923,  067 

58,  209 

12   00 

1,036,536 

68,409 

12   00 

1,021,661 

68,875 

12   00 

1,  006,  475 

69,256 

13   00 

1,122,349 

80,266 

13  00 

1,106,218 

80,811 

13   00 

1,089,752 

81,258 

14   00 

1,208,027 

93,064 

14   00 

1,  190,  636 

93,695 

14   00 

1,  172,  886 

94,  212 

15   00 

1,293,559 

106,802 

15  00 

1,274,904 

107,  525 

15   00 

1,255,866 

108,  117 

16   00 

1,378,934 

121,479 

16   00 

1,359,012 

122,  300 

16   00 

1,  338,  681 

122,  971 

17   00 

1,464,144 

137,093 

17   00 

1,442,949 

138,017 

17   00 

1,421,321 

138,  773 

18   00 

1,549,177 

153,  642 

18   00 

1,526,704        154,675 

18   00 

1,  503,  775 

155,  520 

19   00 

1,634,023 

171,124 

19  00 

1,610,267 

172,  272 

19   00 

,586,031 

173,210 

20   00 

1,  718,  671 

189,  537 

20  00 

1,693,628 

190,805 

20   00 

,  668,  079 

191,841 

21   00 

1,803,113 

208,878 

21   00 

1,776,775 

210,  272 

21   00 

,  749,  909 

211,409 

22   00 

1,887,337 

229,146 

22   00 

1,859,698 

230,  671 

22   00 

,831,509 

231,914 

23   00 

1,971,333 

250,  337 

23   00 

1,942,387 

251,998 

23   00 

1,912,869 

253,  352 

24   00 

2,  055,  091 

272,450 

24   00 

2,  024,  833 

274,  252 

24   00 

1,993,978 

275,  719 

25  00 

2,  138,  602 

295,  481 

25   00 

2,107,023 

297,  430 

25   00 

2,074,826 

299,  014 

26   00 

2,221,854 

319,429          26   00 

2,  188,  948 

321,528 

26   00 

2,  155,  402 

323,  233 

27   00 

2,304,838 

344,  289 

27   00 

2,270,597 

346,543 

27   00 

2,235,695 

348,  374 

28  00 

2,  387,  545 

370,  059 

28  00 

2,351,961 

372,473 

28   00 

2,  315,  695 

374,432 

29  00 

2,469,963 

396,736 

29  00 

2,  433,  029 

399,314 

29   00 

2,  395,  392 

401,404 

30  00 

2,552,084 

424,  317 

30   00 

2,  513,  790 

427,063 

30   00 

2,  474,  774 

429,  287 

46 


GEOGRAPHIC   TABLES    AND    FORMULAS. 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.—  Values  of  X  and  Y  in  meters.    - 

Latitude  42°. 

Latitude  43°. 

Latitude  44°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

•  o    / 

o     / 

O       1 

1   00 

82,851 

484 

1   00 

81,541 

485 

1   00 

80,  206 

486 

2  00 

165,  691 

1,935 

2  00 

163,071 

1,941 

2   00 

160,  401 

1,945 

3   00 

248,508 

4,354 

3   00 

244,  578 

4,367 

3   00 

240,  572 

4,375 

4   00 

331,292 

7,739 

4   00 

326,  050 

7,763 

4   00 

320,708 

7,778 

5   00 

414,030 

12,092 

5   00 

407,  476 

12,  129 

5   00 

400,  797 

12,  152 

6   00 

496,  712 

17,  410 

6   00 

488,  844 

17,  464 

6   00 

480,  827 

17,496 

7   00 

579,325 

23,  693 

7   00 

570,  143 

23,766 

7   00 

560,  786 

23,811 

8   00 

661,  861 

30,  941 

8   00 

651,361 

31,036 

8   00 

640,  662 

31,  094 

9   00 

744,305 

39,  152 

9   00 

732,  486 

39,272 

9   00 

720,  445 

39,  345 

10  00 

826,648 

48,  325 

10   00 

813,508 

48,474 

10   00 

800,122 

48,563 

11   00 

908,  879 

58,  459 

11   00 

894,  415 

58,  639 

11   00 

879,681 

58,  746 

12   00   ' 

990,985 

69,  553 

12   00 

975,  195 

69,  766 

12   00 

959,  110 

69,893 

13   00 

1,072,956 

81,605 

13   00 

1,055,837 

81,854 

13   00 

1,038,399 

82,002 

14   00 

1,  154,  781 

94,  614 

14   00 

1,  136,  329 

94,901 

14   00 

1,  117,  535 

95,072 

15   00 

1,236,449 

108,  577 

15   00 

1,216,661 

108,  905 

.  15   00 

,  196,  507 

109,  100 

16   00 

1,317,948 

123,  493 

16   00 

1,296,820 

123,864 

16   00 

,275,303 

124,084 

17   00 

1,399,267 

139,  360 

17   00 

1,376,795 

139,  777 

17   00 

,  353,  911 

140,023 

18   00 

1,  480,  395 

156,  175 

18   00 

1,  456,  575 

156,  640 

18   00 

,  432,  320 

156,913 

19   00 

1,561,321 

173,  937 

19   00 

1,  536,  148 

174,451 

19   00 

,510,519 

174,753 

20   00 

1,642,035 

192,  642 

20   00 

1,  615,  505 

193,  209 

20   00 

1,  588,  496 

193,  540 

21   00 

1,  722,  524 

212,  289 

21   00 

1,  694,  632 

212,909 

21   00 

1,666,240 

213,  270 

22   00 

1,802,779 

232,  874 

22   00 

1,  773,  519 

233,  551 

22   00 

1,743,738 

233,  942 

23  00 

1,  882,  788 

254,  396 

23   00 

1,852,155 

255,  129 

23   00 

1,820,930 

255,  552 

24   00 

1,962,540 

276,850 

24  00 

1,  930,  528 

277,  642 

24   00 

1,897,955 

278,096 

25  00 

2,  042,  024 

300,  234 

25   00 

2,  008,  628 

301,087 

25   00 

1,974,650 

301,572 

26  00 

2,121,230 

324,  544 

26   00 

2,086,443 

325,  459 

26   00 

2,051,055 

325,  977 

27   00 

2,  200,  146 

349,  778 

27   00 

2,  163,  963 

350,750 

27   00 

2,  127,  159 

351,  306 

28   00 

2,  278,  762 

375,932 

28   00 

2,241,176 

376,  974 

28   00 

2,  202,  950 

377,  555 

29   00 

2,  357,  067 

403,002 

29   00 

2,318,071 

404,109 

29   00 

2,278,417 

404,722 

30   00 

2,435,052 

430,  985 

30   00 

2,  394,  639 

432,  157 

30   00 

2,  353,  550 

432,  801 

GEOGEAPHIC    TABLES    AND    FORMULAS. 


47 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.—  Values  of  X  and  Y  in  meters. 

Latitude  45°. 

Latitude  46°. 

Latitude  47°. 

Longi- 
tude. 

X 

y 

Longi- 
tude. 

X 

Y 

Longi- 
tude, 

X 

Y 

0         / 

1  00 

78,847 

486 

«     / 
1  00 

77,464 

486 

o     / 
1   00 

76,  056 

485 

2  00 

157,  682 

1,946 

2  00 

154,  915 

1,945 

2   00 

152,  100 

1,942 

3  00 

236,  493 

4,378 

3  00 

232,  342 

4,376 

.  3   00 

228,119 

4,368 

4  00 

315,  269 

7,783 

4  00 

309,732 

7,779 

4   00 

304,  101 

7,765 

5   00 

393,9% 

12,  160 

5  00 

387,  074 

12,  153 

5   00 

380,  034 

12,  131 

6   00 

•472,663 

17,508 

6  00 

464,354 

17,  498 

6   00 

455,904 

17,467 

7   00 

501,258 

23,826 

7  00 

541,562 

23,  813 

7   00 

531,700 

23,  770 

8  00 

629,  769 

31,114 

8   00 

<U8,684 

31,0% 

8   00 

607,410 

31,040 

9  00 

708,  184 

39,370 

9   00 

695,  708 

39,  347 

9   00 

683,020 

39,276 

10   00 

786,492 

48,  594 

10   00 

772,623 

48,565 

10   00 

758,  520 

48,  477 

11   00 

864,679 

58,782 

11   00 

849,416 

58,  747 

11   00 

833,  895 

58,640 

12   00 

942,735 

69,936 

12   00 

926,  075 

69,893 

12   00 

909,  135 

69,765 

13  00 

1,020,647 

82,  051 

13   00 

1,002,588 

82,000 

13   00 

984,227 

81,849 

14   00 

1,098,404 

95,  127 

14  00 

1,078,943 

95,067 

14   00 

1,059,158 

94,890 

15   00 

1,175,994 

109,  162 

15  00 

1,  155,  128 

109,  091 

15   00 

,133,917 

108,  887 

16   00 

1,253,404 

124,  153 

15  00 

1,231,131 

124,  071 

16   00 

,208,491 

123,837 

17   00 

,330,624 

140,099 

17   00 

1,306,940 

140,  003 

17   00 

,  282,  868 

139,  738 

18  00 

,  407,  640 

156,9% 

18  00 

1,382,543 

156,887 

18   00 

,  357,  036 

156,  587 

19  00 

,484,443 

174,842 

19   00 

1,  457,  928 

174,718 

19   00 

,  430,  984 

174,  381 

20   00 

,561,019 

193,635 

20   00 

1,533,083 

193,  494 

20   00 

,  504,  697 

193,  118 

21   00 

,637,358 

213,371 

21   00 

1,  607,  997 

213,  212 

21   00 

,  578,  166 

212,  793 

22  00 

,713,447 

234,  048 

22   00 

,  682,  657 

233,  869 

22   00 

,651,377 

233,  405 

23  00 

,789,276 

255,663 

23   00 

,  757,  052 

255,462 

23   00 

,724,320 

254,950 

24  00 

1,864,831 

278,211 

24   00 

,831,170 

277,  987 

24   00 

,  7%,  982 

277,  425 

25  00 

1,940,103 

301,690 

25  00 

,904,999 

301,441 

25   00 

,869,351 

300,824 

26  00 

2,015,079 

326,097 

26   00 

,  978,  528 

325,  820 

26   00 

,941,415 

325,  146 

27   00 

2,  089,  749 

351,  427 

27   00 

2,051,745 

351,  120 

27   00 

2,013,163 

350,  386 

28   00 

2,  164,  100 

377,  676 

28   00 

2,  124,  639 

377,  337 

28   00 

2,084,583 

376,  539 

29   00 

2,  238.  121 

404,841 

29   00 

2,  197,  197 

404,  468 

29   00 

2,  155,  663 

403,  602 

30  00 

2,311,802 

432,  918 

30   00 

2,  269,  410 

432,  507 

30   00 

2,  226,  392 

431,569 

48 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  5. — For  projections  of  maps  of  large  areas — Continued. 
COORDINATES  OF  CURVATURE. 


Natural  scale.—  Values  of  X  and  Y  in  meters. 

Latitude  48°. 

Latitude  49°. 

Latitude  50°. 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

Longi- 
tude. 

X 

Y 

o     / 
1   00 

74,626 

484 

0       > 

1   00 

73,  172 

482 

o     / 
1   00 

71,696 

479 

2   00 

149,  239 

1,936 

2   00 

146,  331 

1,928 

2   00 

143,379 

1,917 

3   00 

223,827 

4,355 

3   00 

•219,465 

4,337 

3   00 

215,037 

4,313 

4   00 

298,  377 

7,  742  • 

4   00 

.     292,  561 

7,709 

4   00 

286,  656 

7,667 

5   00 

372,877 

12,095 

5   00 

365,606 

12,  044 

5   00 

358,  224 

11,  978 

6   00 

447,  314 

17,  414 

6   00 

438,  588 

17,  340 

6   00 

429,  727 

17,246 

7   00 

521,  677 

23,698 

7   00 

511,493 

23,  598 

7   00 

501,154 

23,  469 

8   00 

595,  951 

30,  946 

»   00 

584,  310 

30,  815 

8   00 

572,492 

30,646 

9   00 

670,  125 

39,  157 

9   00 

657,026 

38,991 

9   00 

643,  727 

38,  777 

10   00 

744,  186 

48,329 

10   00 

729,  627 

48,  123 

10   00 

714,  847 

47,  859 

11   00 

818,  123 

58,  461 

11   00 

802,  102 

58,212 

11   00 

785,  839 

57,  891 

12   00 

891,921 

69,  552 

12   00 

874,  438 

69,254 

12   00 

856,691 

68,  872 

13   00 

965,  570 

81,598 

13   00 

946,622 

81,248 

13   00 

927,  389 

80,  798 

14   00 

1,039,056 

94,  598 

14   00 

1,018,642 

94,  191 

14   00 

997,  922 

93,  669 

15   00 

1,112,367 

108,  551 

15   00 

1,090,485 

108,  082 

15   00 

1,068,277 

107,  482 

16   00 

1,185,491 

123,453 

16   00 

1,162,138 

122,  918 

16   00 

1,138,440 

122,234 

17   00 

1,258,416 

139,  302 

17   00 

1,  233,  591 

138,  697 

17   00 

1,208,400 

137,  923 

18   00 

1,331,129 

156,096 

18   00 

1,304,829 

155,416 

18   00 

1,  278,  144 

154,546 

19   00 

1,  403,"618 

173,832 

19   00 

1,375,840 

173,  071 

19   00 

1,347,660 

172,  099 

20   00 

,  475,  871 

192,506 

20   00 

1,446,613 

191,660 

20   00 

1,416,934 

190,581 

21   00 

,547,876 

212,  116 

21   00 

1,517,135 

211,  180 

21   00 

1,485,956 

209,  987 

22   00 

,619,620 

232,  658 

22   00 

1,587,394 

231,627 

22   00 

1,554,711 

230,  314 

23   00 

,691,091 

254,  128 

23   00 

1,657,378 

252,  998 

23   00 

1,  623,  189 

251,559 

24   00 

,  762,  279 

276,  524 

24   00 

1,727,073 

275,288 

24   00 

1,691,377 

273,  717 

25   00 

1,833,170 

299,842 

25   00 

1,  796,  470 

298,  495 

25   00 

1,759,262 

296,  785 

26   00 

1,903,752 

324,  077 

26   00 

1,865,554 

322,614 

26   00 

1,826,833 

320,  758 

27   00 

1,974,015 

349,225 

27   00 

1,934,315 

347,  640 

27   00 

1,894,077 

345,  633 

28   00 

2,  043,  945 

375,283 

28   00 

2,  002,  740 

373,  570 

28   00 

1,960,983 

371,404 

29   00 

2,  113,  531 

402,245 

29   00 

2,  070,  817 

400,  399 

29   00 

2,  027,  538 

398,068 

30   00 

2,  182,  762 

430,  107 

30   00 

2,  138,  536 

428,  123 

30   00 

2,  093,  731 

425,  619 

GEOGRAPHIC   TABLES    AND    FORMULAS. 


49 


TABLE  6.— Coordinates  for  projection  of  maps  (scale 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 
0    00 
10 
20 
30 
40 
50 

1    00 
10 
20 
30 
40 
50 

2    00 
10 
20 
30 
40 
50 

3    00 
10 
20 
30 
40 
50 

4    00 
10 
20 
30 
40 
50 

5    00 
10 
20 
30 
40 
50 

6    00 
10 
20 
30 
40 
50 

7    00 
10 
20 
30 
40 
50 

8    00 

Inches. 

Inches. 
2.922 
2.922 
2.922 
2.922 
2.922 
2.921 

2.921 
2.921 
2.921 
2.921 
2.920 
2.920 

2.920 
2.920 
2.919 
2.919 
2.918 
2.918 

2.918 
2.917 
2.917 
2.916 
2.916 
2.915 

2.915 
2.914 
2.913 
2.913 
2.912 
2.911 

2.911 
2.910 
2.909 
2.908 
2.908 
2.907 

2.906 
2.905 
2.904 
2.903 
2.902 
2.901 

2.900 
2.899 
2.898 
2.897 
2.896 
•2.  S'.)f> 

2.894 

Inches. 
5.844 
5.843 
5.843 
5.843 
5.843 
5.843 

5.843 
5.842 
5.842 
5.841 
5.841 
5.840 

5.840 
5.839 
5.839 
5.838 
5.837 
5.836 

5.836 
5.835 
5.834 
5.832 
5.831 
5.830 

5.829 
5.828 
5.827 
5.825 
5.824 
5.823 

5.822 
5.820 
5.818 
5.817 
5.815 
5.813 

5.812 
5.810 
5.808 
5.806 
5.804 
5.802 

5.800 
5.798 
5.7% 
5.794 
5.791 
5.789 

5.787 

Inches. 
8.765 
8.765 
8.765 
8.765 
8.764 
8.764 

8.764 
8.763 
8.763 
8.762 
8.761 
8.761 

8.760 
8.759 
8.758 
8.757 
8.756 
8.755 

8.753 
8.752 
8.750 
8.749 
8.747 
8.746 

8.744 
8.  742 
8.740 
8.738 
8.736 
8.734 

8.732 
8.730 
8.727 
8.725 
8.722 
8.720 

8.718 
8.715 
8.  712 
8.709 
8.706 
8.703 

8.701 
8.697 
8.604 
8.6% 
8.687 
8.684 

8.680 

Inches. 
11.687 
11.687 
11.686 
11.686 
11.686 
11.686 

11.685 
11.684 
11.684 
11.683 
11.682 
11.681 

11.680 
11.678 
11.677 
11.676 
11.  674 
11.  673 

11.671 
11.669 
11.  667 
11.665 
11.663 
11.661 

11.659 
11.656 
11.654 
11.651 
11.648 
11.646 

11.643 
11.640 
11.636 
11.633 
11.630 
11.  627 

11.  624 
11.620 
11.616 
11.612 
11.608 
11.604 

11.601 
11.596 
11.592 
11.587 
11.  583 
11.  578 

11.574 

Inches. 
14.609 
14.  608 
14.608 
14.608 
14.608 
14.607 

14.606 
14.606 
14.604 
14.604 
14.602 
14.601 

14.600 
14.  598 
14.5% 
14.594 
14.  592 
14.  591 

14.589 
14.586 
14.584 
14.581 
14.  578 
14.  576 

14.  574 
14.  570 
14.567 
14.564 
14.560 
14.557 

14.554 
14.550 
14.546 
14.  542 
14.538 
14.534 

14.  530 
14.  524 
14.  520 
14.  515 
14.510 
14.506 

14.501 
14.  496 
14.490 
14.  484 
14.  478 
14.  473 

14.  468 

Inches. 
17.  531 
17.530 
17.  530 
17.530 
17.  529 
17.528 

17.  528 
17.  527 
17.  525 
17.524 
17.  522 
17.  521 

17.  520 
17.518 
17.516 
17.  513 
17.  511 
17.509 

17.507 
17.504 
17.501 
17.  497 
17.  494 
17.  491 

17.488 
17.  484 
17.480 
17.  476 
17.473 
17.468 

17.465 
17.  459 
17.455 
17.450 
17.  445 
17.440 

17.435 
17.  429 
17.  424 
17.418 
17.413 
17.407 

17.401 
17.  395 
17.387 
17  381 
17.374 
17.3b8 

17.  361 

Longi- 
tude 
inter- 
val. 

0° 

1° 

5.804 
11.608 
17.  412 
23.216 
29.020 

5 
10 
15 
20 
25 
30 

Inches. 
0.000 
.000 
.000 
.000 
.000 
.000 

Inches. 
0.000 
.000 
.000 
.001 
.001 
.001 

5.840 
11.608 
17.412 
23.216 
29.020 

2° 

3° 

5.804 
11.608 
17.412 
23.216 
29.020 

"~5."  804" 
11.608 
17.413 
23.217 
29.021 

5 
10 
15 
,20 
25 
30 

0.000 
.000 
.001 
.001 
.002 
.003 

0.000 
.000 
.001 
.002 
.003 
.004 

4° 

5° 

5.804 
11.609 
17.  413 
23.217 
29.022 

5 
10 
15 

20 
25 
30 

0.000 
.001 
.001 
.002 
.004 
.005 

0.000 
.001 
.002 
.003 
.005 
.007 

5.804 
11.609 
17.414 
23.218 
29.022 

6° 

7o 

5 
10 
15 
20 
25 
30 

0.000 
.001 
.002 
.004 
.006 
.008 

0.000 
.001 
.002 
.004 
.006 
.009 

5.805 
11.609 
17.414 
23.219 
29.024 

8° 

5.805 
11.610 
17.  415 
23.220 
29.025 

5 
10 
15 
20 
25 
30 

0.000 
.001 
.003 
.005 
.007 
.'010 

46061—08- 


50 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


TABLE  6. — Coordinates  for  projection  of  maps  (scale  T2sVoo) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

O         ' 

8    00 
10 
20 
30 
40 
50 

9    00 
10 
20 
30 
40 
50 

10    00 
10 
20 
30 
40 
50 

11    00 
10 
20 
30 
40 
50 

12    00 
10 
20 
30 
40 
50 

13    00 
10 
20 
30 
40 
50 

14    00 
10 
20 
30 
40 
50 

15    00 
10 
20 
30 
40 
50 

16    00 

Inches. 

Inches. 
2.894 
2.892 
2.891 
2.890 
2.888 
2.887 

2.886 
2.885 
2.883 
2.882 
2.881 
2.879 

2.878 
2.876 
2.875 
2.873 
2.872 
2.870 

2.869 
2.  867 
2.865 
2.864 

2.862 
2.860 

2.858 
2.857 
2.855 
2.853 
2.851 
2.849 

2.847 
2.846 
2.844 
2.842 
2.840 
2.838 

2.836 
2.834 
2.831 

2.829 
2.827 
2.825 

2.823 

2.821 
2.818 
2.816 
2.814 
2.812 

2.809 

Inches. 

5.787 
5.784 
5.782 
5.779 
5.777 
5.775 

5.772 
5.769 
5.767 
•5.764 
5.761 
5.758 

5.755 
5.752 
5.749 
5.  746 
5.743 
5.740 

5.  737 
5.734 
5.730 
5.727 
5.724 
5.720 

5.717 
5.713 
5.709 
5.706 
5.  702 
5.698 

5.695 
5.691 
6.687 
5.683 
5.679 
5.675 

5.671 
5.667 
5.663 
5.658 
5.654 
5.650 

5.646 
5.641 
5.637 
5.632 
5.628 
5.623 

5.  619 

Inches. 
8.680 
8.677 
8.673 
8.669 
8.666 
8.662 

8.658 
8.654 
8.650 
8.646 
8.642 
8.637 

8.633 
8.628 
8.624 
8.619 
8.614 
8.610 

8.606 
8.601 
8.596 
8.590 
8.585 
8.580 

8.575 
8.570 
8.564 
8.559 
8.  553 
8.  548 

8.542 
8.536 
8.530 
8.  524 
8.519 
8.  513 

8.507 
8.500 
8.494 
8.488 
8.481 
8.475 

8.469 
8.462 
8.455 
8.448 
8.441 
8.435 

8.428 

Inches. 
11.  574 
11.569 
11.564 
11.  559 
11.554 
11.549 

11.544 
11.539 
11.533 
11.  528 
11.522 
11.  516 

11.511 
11.504 
11.  498 
11.492 
11.486 
11.  480 

11.  474 
11.468 
11.461 
11.454 
11.447 
11.440 

11.434 
11.  426 
11.419 
11.412 
11.404 
11.397 

11.390 
11.  382 
11.  374 
11.  366 
11.358 
11.350 

11.342 
11.334 
11.  326 
11.317 
11.308 
11.300 

11.292 
11.  282 
11.274 
11.264 
11.255 
11.  246 

11.  237 

Inches. 
14.  468 
14.  461 
14.  455 
14.  448 
14.  442 
14.  436 

14.  430 
14.424 
14.  416 
14.410 
14.  402 
14.  396 

14.388 
14.380 
14.  373 
14.  366 
14.  358 
14.350 

14.  342 
14.  334 
14.  326 
14.  318 
14.309 
14.300 

14.  292 
14.  282 
14.  274 
14.  264 
14.  256 
14.  246 

14.  237 
14.  228 
14.  218 
14.  208 
14.  198 
14.  188 

14.178 
14.  168 
14.157 
14.  146 
14.  136 
14.  125 

14.114 
14.  103 
14.  092 
14,080 
14.  069 
14.  058 

14.046 

Inches. 
17.  361 
17.  353 
17.  346 
17.  338 
17.  331 
17.  324 

17.317 
17.  308 
17.300 
17.291 
17.283 
17.  275 

17.  266 
17.257 
17.  248 
17.  239 
17.  229 
17.  220 

17.211 
17.201 
17.  191 
17.181 
17.  171 
17.  161 

17.  150 
17.  139 
17.  128 
17.  117 
17.  107 
17.  095 

17.  084 
17.  073 
17.  061 
17.  049 
17.038 
17.  026 

17.  014 
17.  001 

16.  988 
16.  975 
16.  963 
16.950 

16.  937 
16.  924 
16.910 
16.  897 
16.883 
16.  870 

16.  856 

Longi- 
tude 
inter- 
val. 

8° 

9° 

5.  805 
11.610 
17.  416 
23.221 
29.  026 

""5."  806" 
11.611 
17.417 
23.222 
29.  028 

5 
10 
15 
20 
25 
30 

Inches. 
0.000 
.001 
.003 
.005 
.007 
.010 

Inches. 
0.000 
.001 
.003 
.005 
.008 
.012 

10° 

11° 

0.000 
.002 
.004 
.006 
.010 
.014 

5.806 
11.  612 
17.417 
23.223 
29.  029 

5 
10 
15 
20 
25 
30 

0.000 
.001 
.003 
.006 
.009 
.013 

5.806 
11.612 
17.  419 
23.  225 
29.  031 

12° 

13° 

5 
10 
15 
20 
25 
30 

0.000 
.002 
.004 
.007 
.011 
.016 

0.000 
.002 
.004 
.007 
.012 
.017 

5.807 
11.613 
17.  420 
23.226 
29.  033 

5.807 
11.614 
17.421 
23.  228 
29.035 

14° 

15° 

5 
10 
25 
20 
25 
30 

0.000 
.002 
.004 
.008 
.012 
.018 

0.001 
.002 
.005 
.009 
.013 
.019 

5.808 
11.615 
17.  422 
23.  230 
29.  038 

16° 

5.808 
11.616 
17.  424 
23.  232 
29.  040 

5 
10 
15 
20 
25 
30 

0.001 
.002 
.005 
.009 
.014 
.020 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  6. — Coordinates  for  projection  of  maps  (scale  j^V^o") — Continued. 
[From  Smithsonian  Geographical  Tables.] 


51 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 
16    00 
10 
20 
30 
40 
50 

17    00 
10 
20 
30 
40 
50 

18    00 
10 
20 
30 
40 
50 

19    00 
10 
20 
30 
40 
50 

20    00 
10 
20 
30 
40 
50 

21    00 
10 
20 
30 
40 
50 

22    00 
10 
20 
30 
40 
50 

23    00 
10 
20 
30 
40 
50 

24    00 

Inches. 

Inches. 
2.809 
2.807 
2.804 
2.802 
2.800 
2.797 

2.795 
2.792 
2.790 

2.787 
2.785 
2.782 

2.780 
2.777 
2.  774 
2.772 
2.769 
2.766 

2.764 
2.761 
2.758 
2.755 
2.752 
2.750 

2.747 
2.743 
2.741 
2.738 
2.735 
2.  732 

2.  729 
2.  72C 
2.  723 
2.720 
2.717 
2.714 

2.710 
2.707 
2.  704 
2.701 
2.697 
2.694 

2.691 

2.688 
2.684 
2.681 
2.677 
2.674 

2.671 

Inches. 
5.619 
5.614 
5.609 
5.604 
5.599 
5.595 

5.590 
5.585 
5.580 
5.575 
5.570 
5.564 

5.559 
5.554 
5.549 
5.M3 
5.538 
5.533 

5.527 
5.522 
5.516 
5.510 
5.505 
5.499 

5.493 
5.487 
5.482 
5.476 
5.470 
5.464 

5.458 
5.452 
5.445 
5.439 
5.433 
5.427 

5.421 
5.414 
5.408 
5.401 
5.395 
5.388 

5.382 
5.375 
5.368 
5.362 
5.355 
5.348 

5.341 

Inches. 
8.428 
8.421 
8.414 
8.406 
8.399 
8.392 

8.385 
8.377 
8.369 
8.362 
8.354 
8.347 

8.339 
8.331 
8.323 
8.315 
8.307 
8.299 

8.291 
8.282 
8.274 
8.266 
8.257 
8.  249 

8.240 
8.231 
8.  222 
8.213 
8.204 
8.1% 

8.187 
8.177 
8.168 
8.159 
8.150 
8.141 

8.131 
8.122 
8.112 
8.102 
8.092 
8.083 

8.  073 
8.063 
8.053 
8.042 
8.032 
8.022 

8.012 

Inches. 
11.237 
11.228 
11.218 
11.208 
11.199 
11.  189 

11.  180 
11.  170 
11.159 
11.149 
11.  139 
11.  129 

11.  119 
11.108 
11.097 
11.087 
11.  076 
11.065 

11.054 
11.  043 
11.032 
11.021 
11.009 
10.  998 

10.  987 
10.  975 
10.  963 
10.  951 
10.  939 
10.928 

10.  916 
10.903 
10.891 
10.  878 
10.  866 
10.  854 

10.  842 
10.829 
10.  816 
10.  802 
10.790 
.10.777 

10.764 
10.750 
10.  737 
10.  723 
10.710 
10.  696 

10.  683 

Inches. 
14.  046 
14.  034 
14.  022 
14.  010 
13.  998 
13.  986 

13.  974 
13.  962 
13.  949 
13.  936 
13.924 
13.911 

13.  898 
13.  885 
13.  872 
13.859 
13.845 
13.832 

13.818 
13.804 
13.790 
13.  776 
13.  762 
13.  748 

13.  734 
13.719 
13.  704 
13.  689 
13.  674 
13.  660 

13.  645 
13.  629 
13.  614 
13.  598 
13.  583 
13.  568 

13.  552 
13.  536 
13.  520 
13.503 
13.487 
13.  471 

13.  455 
13.  438 
13.  421 
13.  404 
13.387 
13.  371 

13.354 

Inches. 
16.856 
16.  841 
16.  827 
16.813 
16.  798 
16.  784 

16.  769 
16.  754 
16.  739 
16.  724 
16.709 
16.  693 

16.  678 
16.  662 
16.646 
16.  630 
16.614 
16.  598 

16.582 
16.565 
16.548 
16.  531 
16.  514 
16.  497 

16.  480 
16.  462 
16.445 
16.  427 
16.  409 
16.  391 

16.  373 
16.  355 
16.  336 
16.  318 
16.300 
16.  281 

16.  262 
16.  243 
16.  223 
16.  204 
16.184 
16.  165 

16.  145 
16.  125 
16.  105 
16.  085 
16.  064 
16.  045 

16.  024 

Longi- 
tude 
inter- 
val. 

16° 

17° 

5.809 
11.617 
17.  426 
23.234 
29.043 

5 
10 
15 
20 

25 
30 

Inches. 
0.001 
.002 
.005 
.009 
.014 
.020 

Inches. 
0.001 
,    .002 
.005 
.010 
.015 
.021 

5.809 
11.618 
17.  427 
23.236 
29.046 

18° 

19° 

5.810 
11.619 
17.  429 
23.  239 
29.049 

5 
10 
15 
20 
25 
30 

0.001 
.002 
.006 
.010 
.016 
.022 

0.001 
.003 
.006 
.010 
.016 
.024 

5.810 
11.621 
17.  431 
23.242 
29.  052 

20° 

21° 

5 
10 
15 
20 
25 
30 

o.  061 

.003 
.006 
.011 
.017 
.025 

0.001 
.003 
.006 
.011 
.018 
026 

5.811 
11.622 
17.433 
23.  244 
29.055' 

5.  812 
11.623 
17.  435 
23.247 

29.  058 

22° 

23° 

5 
10 
15 

20 
25 
30 

0.001 
.003 
.007 
.  012 
.018 
.027 

0.001 
.003 
.007 
.012 
.019 
.028 

5.  812 
11.625 
17.437 
23.  250 
29.  062 

"~5.'813' 
11.626 
17.439 
23.  252 
29.066 

24° 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.007 
.013 
.020 
.028 

52 


GEOGRAPHIC   TABLES    AND   FORMULAS. 


TABLE  6. — Coordinates  for  projection  of  maps  (scale  TITTTOTT) — Continued 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

0          / 

24    00 
10 
20 
30 

40 
50 

25    00 
10 
20 
30 
40 
50 

26    00 
10 
20 
30 
40 
50 

27    00 
10 
20 
30 
40 
50 

28    00 
10 
20 
30 
40 
50 

29    00 
10 
20 
30 
40 
50 

30    00 
10 
20 
30 
40 
50 

31    00 
10 
20 
30 
40 
50 

32    00 

Inches. 

"'5~8i4' 
11.  628 
17.442 
23.256 
29.069 

Inches. 
2.671 
2.667 
2.664 
2.660 
2.657 
2.653 

2.650 
2.646 
2.642 
2.  639 
2.635 
2.631 

2.628 
2.624 
2.620 
2.616 
2.613 
2.609 

2.605 
2.  601 
2.597 
2.593 
2.589 
2.586 

2.582 
2.578 
2.574 
2.570 
2.566 
2.562 

2.558 
2.553 
2.549 
2.545 
2.541 
2.537 

2.533 
2.528 
2.524 
2.520 
2.515 
2.511 

2.507 
2.502 
2.498 
2.493 
2.489 
2.485 

2.480 

Inches. 
5.341 
5.334 
5.327 
5.320 
5.313 
5.306 

5.299 
5.292 
5.285 
5.278 
5.270 
5.263 

5.256 
5.248 
5.240 
5.233 
5.225 
5  218 

5.210 
5.203 
5.195 
5.187 
5.179 
5.171 

5.163 
5.155 
5.147 
5.139 
5.131 
5.123 

5.115 
5.107 
5.098 
5.090 
5.082 
5.073 

5.065 
5.056 
5.048 
5.  039 
5.  031 
5.022 

5.014 
5.005 
4.996 
4.987 
4.978 
4.969 

4.960 

Inches. 
8.  012 
8.002 
7.991 
7.981 
7.970 
7.960 

7.949 

7.938 
7.927 
7.916 
7.905 
7.894 

7.883 
7.872 
7.861 
7.849 
7.838 
7.827 

7.816 
7.  804 
7.792 

7.780 
7.768 
7.757 

7.745 
7.733 
7.721 
7.709 
7.697 
7.685 

7.  673  ' 
7.660 
7.648 
7.635 
7.622 
7.610 

7.598 
7.585 
7.572 
7.  559 
7.546 
7.533 

7.520 
7.507 
7.494 
7.480 
7.46T 
7.454 

7.441 

Inches. 
10.683 
10.  669 
10.655 
10.641 
10.  627 
10.613 

10.599 
10.584 
10.  570 
10.555 
10.  540 
10.  526 

10.  511 
10.  496 
10.  481 
10.  466 
10.  451 
10.  436 

10.  421 
10.  405 
10.390 
10.374 
10.358 
10.  342 

10.  327 
10.  311 
10.294 
10.  278 
10.  262 
10.  246 

10.  230 
10.  213 
10.  197 
10.180 
10.  163 
10.  146 

10.  130 
10.  113 
10.  096 
10.  078 
10.061 
10.  044 

10.  027 
10.009 
9.992 
9.974 
9.956 
9.938 

9.921 

Inches. 
13.  354 
13.  336 
13.  319 
13.  301 
13.284 
13.  266 

13.  249 
13.  231 
13.212 
13.  194 
13.  176 
13.  157 

13.  139 
13.  120 
13.  101 
13.  082 
13.063 
13.  045 

13.026 
13.006 
12.  987 
12.  967 
12.  947 
12.928 

12.909 
12.889 
12.868 
12.  848 
12.828 
12.808 

12.  788 
12.  767 
12..746 
12.  725 
12.704 
12.683 

12.  662 
12.641 
12.  620 
12.  598 
12.577 
12.555 

12.  534 
12.  512 
12.490 
12.  467 
12.445 
12.  423 

12.401 

Inches. 
16.024 
16.003 
15.  982 
15.  961 
15.  940 
15.  919 

15.  898 
15.  877 
15.854 
15.  833 
15.811 
15.788 

15.  767 
15.  744 
15.  721 
15.  698 
15.  676 
15.654 

15.  631 
15.  608 
15.584 
15.560 
15.  537 
15.514 

15.490 
15.466 
15.442 
15.418 
15.394 
15.369 

15.345 
15.  320 
15.295 
15.  270 
15.  245 
15.  220 

15.  195 
15.  169 
15.  143 
15.  118 
15.092 
15.066 

15.040 
15.  014 
14.987 
14.  960 
14.  934 
14.908 

14.881 

Longi- 
tude 
inter- 
val. 

24° 

25° 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.003 
.007 
.013 
.020 
.028 

Inches. 
0.001 
.003 
.007 
.013 
.020 
.029 

5.815 
11.629 
17.  444 
23.259 
29.  074 

26° 

27° 

5.  816 
11.  631 
17.446 
23.262" 
29.  077 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.008 
.013 
.021 
.030 

0.001 
.003 
.008 
.014 
.022 
.031 

5.816 
11.633 
17.  449 
23.265 
29.082 

28° 

29° 

5 
10 
15 
20 
25' 
•     30 

0.001 
.004 
.008 
.014 
.022 
.032 

0.001 
.004 
.008 
.014 
.023 
.032 

5.817 
11.  634 
17.  451 
23.268 
29.  086 

5.818 
Ik  636 
17.454 
23.272 
29.090 

30° 

31° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.008 
.015 
.023 
.033 

0.001 
.004 
.008 
.015 
.023 
.034 

5.819 
11.  638 
17.457 
23.276 
29.094 

32° 

5.820 
11.640 
17.460 
23.  280 
29.  100 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.015 
.024 
.034 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  6. — Coordinates  for  projection  of  maps  (scale  T^nnr) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


53 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

W  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 
32    00 
10 
20 
30 
40 
50 

33    00 
10 
20 
30 
40 
50 

34    00 
10 
20 
30 
40 
50 

35    00 
10 
20 
30 
40 
50 

36    00 
10 
20 
30 
40 
50 

37    00 
10 
20 
30 
40 
50 

38    00 
10 
20 
30 
40 
50 

39    00 
10 
20 
30 
40 
50 

40    00 

Inches. 

Inches. 
2.480 
2.476 
2.471 
2.467 
2.462 
2.458 

2.453 
2.448 
2.444 
2.439 
2.434 
2.429 

2.425 

2.420 
2.415 
2.410 
2.406 
2.401 

2.396 
2.391 
2.386 
2.381 
2.377 
2.372 

2.367 
2.362 
2.357 
2.351 
2.346 
2.341 

2.336 
2.331 
2.326 
2.321 
2.316 
2.311 

2.305 
2.300 
2.295 
2.290 
2.  284 
2.279 

2.274 
2.268 
2.263 
2.258 
2.252 
2.247 

2.241 

Inches. 
4.960 
4.951 
4.942 
4.933 
4.924 
4.915 

4.906 
4.896 
4.887 
4.878 
4.868 
4.859 

4.850 
4.840 
4.830 
4.821 
4.811 
4.802 

4.792 
4.  782 
4.773 
4.763 
4.753 
4.743 

4.733 
4.723 
4.713 
4.703 
4.693 
4.683 

4.673 
4.662 
4.652 
4.642 
4.631 
4.621 

4.611 
4.600 
4.590 
4.579 
4.568 
4.558 

4.548 
4.537 
4.526 
4.515 
4.504 
4.493 

4.483 

Inches. 
7.441 
7.427 
7.413 
7.400 
7.386 
7.373 

7.359 
7.345 
7.331 
7.316 
7.302 
7.288 

7.274 
7.260 
7.246 
7.231 
7.217 
7.203 

7.188 
7.174 
7.159 
7.144 
7.130 
7.115 

7.099 
7.085 
7.070 
7.055 
7.039 
7.024 

7.009 
6.994 
6.978 
6.963 
6.947 
6.932 

6.916 
6.900 
6.884 
6.869 
6.853 
6.837 

6.821 
6.805 
6.789 
6.773 
6.756 
6.740 

6.724 

Inches. 
9.921 
9.903 
9.884 
9.866 
9.848 
9.830 

9.812 
9.793 
9.774 
9.  755 
9.736 
9.718 

9.699 
9.680 
9.661 
9.642 
9.622 
9.604 

9.584 
9.565 
9.545 
9.526 
9.506 
9.486 

9.466 
9.446 
9.426 
9.406 
9.386 
9.366 

9.345 
9.325 
9.304 
9.284 
9.263 
9.242 

9.222 
9.200 
9.179 
9.158 
9.137 
9.116 

9.095 
9.073 
9.052 
9.030 
9.008 
8.987 

8.965 

Inches. 
12.  401 
12.379 
12.355 
12.  333 
12.  310 
12.288 

12.265 
12.241 
12.  218 
12.194 
12.  171 
12.  147 

12.  124 
12.100 
12.  076 
12.052 
12.028 
12.004 

11.980 
11.956 
11.  932 
11.907 
11.883 
11.858 

11.833 
11.808 
11.  783 
11.  757 
11.  732 
11.707 

11.682 
11.656 
11.630 
11.605 
11.579 
11.553 

11.527 
11.501 
11.  474 
11.448 
11.421 
11.395 

11.  369 
11.  342 
11.315 
11.288 
11.  261 
11.234 

11.207 

Inches. 
14.881 
14.854 
14.  827 
14.800 
14.  772 
14.  745 

14.  717 
14.689 
14.661 
14.  633 
14.  605 
14.  576 

14.549 
14.  520 
14.491 
14.  462 
14.434 
14.405 

14.  376 
14.  347 
14.  318 
14.288 
14.  259 
14.  230 

14.200 
14.  170 
14.  139 
14.109 
14.  078 
14.  048 

14.  018 
13.  987 
13.956 
13.  925 
13.894 
13.864 

13.832 
13.801 
13.  769 
13.  737 
13.  705 
13.  673 

13.642 
13.  610 
13.  577 
13.545 
13.  513 
13.480 

13.448 

Longi- 
tude 
inter- 
val. 

32° 

33° 

5.821 
11.642 
17.462 
23.283 
29.104 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.004 
.009 
.015 
.024 
.034 

Inches. 
0.001 
.004 
.009 
.016 
.024 
.035 

5.822 
11.643 
17.465 
23.287 
29.109 

34° 

35° 

5.823 
11.645 
17.468 
23.291 
29.113 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.016 
.025 
.036 

0.001 
.004 
.009 
.016 
.025 
.036 

5.824 
11.647 
17.471 
23.294 
29.118 

36° 

37° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.013 
.025 
.036 

0.001 
.004 
.009 
.016 
.026 
.   .037 

5.824 
11.649 
17.  473 
23.297 
29.122 

5.826 
11.651 
17.  477 
23.302 
29.128 

38° 

39° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.017 
.026 
.037 

0.001 
.004 
.009 
.017 
.026 
.037 

5.827 
11.653 
17.480 
23.306 
29.133 

40° 

5.828 
11.655 
17.483 
23.310 
29.138 

5 
10 
15 

20' 
25 
30 

0.001 
.004 
.009 
.017 
.026 
.038 

54 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  6.— Coordinates  for  projection  of  maps  (scale  T^\nnj)  —Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'longi 
tude. 

20'longi 
tude. 

25'  longi- 
tude. 

30'longi 
tude. 

o      / 
40    00 
10 
20 
30 
40 
50 

41    00 
10 
20 
30 
40 
50 

42    00 
10 
20 
30 
40 
50 

43    00 
10 
20 
30 
40 
50 

44    00 
10 
20 
30 
40 
50 

45    00 
10 
20 
30 
40 
50 

46    00 
10 
20 
30 
40 
50 

47    00 
10 
20 
30 
40 
50 

48    00 

Inches. 

Inches. 
2.241 
2.236 
2.230 
2.225 
2.219 
2.214 

2.208 
2.203 
2.197 
2.192 
2.186 
2.180 

2.175 
2.169 
2.163 
2.  157 
2.  152 
2.146 

2.140 
2.135 
2.129 
2.123 
2.117 
2.111 

2.105 
2.099 
2.  093 
2.087 
2.081 
2.076 

2.070 
2.064 
2.057 
2.051 
2.045 
2.039 

2.033 
2.027 
2.021 
2.015 
2.009 
2.003 

1.996 
.990 
.984 
.978 
.971 
.965 

1.959 

Inches. 
4.483 
4.472 
4.461 
4.450 
4.439 
4.428 

4.417 
4.406 
4.394 
4.383 
4.372 
4.360 

4.349 
4.338 
4.326 
4.315 
4.303 
4.292 

4.281 
4.269 
4.257 
4.246 
4.234 
4.222 

4.210 
4.199 
4.187 
4.  175 
4.163 
4.151 

4.139 
4.127 
4.115 
4.103 
4.091 
4.079 

4.067 
4.054 
4.042 
4.030 
4.017 
4.005 

3.992 
3.980 
3.968 
3.955 
3.943 
3.930 

3.917 

Inches. 
6.724 
6.707 
6.691 
6.674 
6.658 
6.641 

6.625 
6.608 
6.591 
6.575 
6.558 
6.541 

6.524 
6.507 
6.490 
6.472 
6.455 
6.438 

6.421 
6.403 
6.386 
6.368 
6.351 
6.333 

6.316 
3.  298 
6.280 
6.262 
6.244 
6.227 

6.209 
6.191 
6.172 
6.154 
6.136 
6.118 

6.100 
6.081 
6.063 
6.044 
6.026 
6.008 

5.989 
5.970 
5.951 
5.933 
5.  914 
5.895 

5.876 

Inches. 
8.  965 
8.943 
8.921 
8.899 
8.877 
8.855 

8.834 
8.811 
8.788 
8.766 
8.744 
8.721 

8.698 
8.676 
8.653 
8.630 
8.607 
8.584 

8.561 
8.538 
8.514 
8.491 
8.468 
8.444 

8.421 
8.397 
8.373 
8.350 
8.326 
8.302 

8.278 
8.254 
8.230 
8.206 
8.181 
8.157 

8.133 
8.108 
8.084 
8.059 
8.034 
8.010 

7.985 
7.960 
7.935 
7.910 
7.885 
7.860 

7.835 

Inches. 
11.  207 
11.  179 
11.  152 
11.  124 
11.097 
11.069 

11.042 
11.  014 
.    10.985 
10.  958 
10.  929 
10.901 

10.  873 
10.844 
10.  816 
10.  787 
10.  759 
10.730 

10.702 
10.  672 
10.  643 
10.  614 
10.585 
10.  556 

10.  526 
10.  496 
10.  467 
10.  437 
10.407 
10.  378 

10.  348 
10.  317 
10.  288 
10.  257 
10.  226 
10.  197 

10.  166 
10.  136 
10.  104 
10.  074 
10.  043 
10.  013 

9.981 
9.951 
9.919 
9.888 
9.857 
9.826 

9.794 

Inches. 
13.448 
13.415 
13.  382 
13.  349 
13.316 
13.283 

13.250 
13.217 
13.183 
13.  149 
13.  115 
13.  081 

13.  048 
13.  013 
12.  979 
12.  945 
12.  910 
12.  876 

12.842 
12.807 
12.  772 
12.  737 
12.  701 
12.  667 

12.  631 
12.  596 
12.  560 
12.  524 
12.  489 
12.  453 

12.  417 
12..381 
12.  345 
12.308 
12.  272 
12.236 

12.  199 
12.163 
12.  125 
12.  089 
12.  052 
12.  015 

11.  978 
11.941 
11.903 
11.  866 
11.  828 
11.  791 

11.  752 

Longi- 
tude 
inter- 
val. 

40° 

41° 

5.829 
11.657 
17.  486 
23.  314 
29.  143 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.004 
.009 
.017 
.026 
.038 

Inches. 
0.001 
.004 
.009 
.017 
.026 
.038 

5.830 
11.  659 
17.  489 
23.319 
29.  149 

42° 

43° 

5.831 
11.661 
17.  492 
23.  323 
29.154 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.010 
.017 
.026 
.038 

0.001 
.004 
.010 
.017 
.027 
.038 

5.  832 
11.  663 
17.  495 
23.327 
29.  159 

44° 

45° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.010 
.017 
.027 
.038 

0.001 
.004 
.010 
.017 
.027 
.038 

5.833 
11.666 
17.  498 
23.  331 
29.  164 

5.834 
11.  668 
17.501 
23.335 
29.  169 

46° 

47° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.010 
.017 
.027 
.038 

0.001 
.004 
.010 
.017 
.027 
.038 

5.835 
11.  670 
17.504 
23.  339 
29.  174 

""5."  836* 
11.  672 
17.508 
23.  344 
29.  180 

48° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.010 
.017 
.026 
.038 

GEOGRAPHIC    TABLES    AND   FORMULAS. 

TABLE  6. — Coordinates  for  projection  of  maps  (scale  i^-sWo) — Continued. 


55 


[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

0          / 

48    00 
10 
20 
30 
40 
50 

49    00 
10 

•20 
30 
40 
50 

50    00 
10 
20 
30 
40 
50 

51    00 
10 
20 
30 
40 
50 

52    00 
10 
20 
30 
40 
50 

53    00 
10 
20 
30 
40 
50 

54    00 
10 
20 
30 
40 
50 

55    00 
10 
20 
30 
40 
50 

56    00 

Inches. 

Inches. 
1.959 
1.952 
1.946 
1.940 
1.933 
1.927 

1.921 
1.914 
1.908 
1.901 
1.895 
1.888 

1.882 
1.875 
1.869 
1.862 
1.856 
1.849 

1.842 
1.836 
1.829 
1.823 
1.816 
1.809 

1.803 
1.796 
1.789 
1.782 
1.776 
1.769 

1.762 
1.755 
1.748 
1.742 
1.735 
1.728 

1.721 
1.714 
1.707 
1.700 
1.  694 
1.687 

1.680 
1.673 
1.666 
1.659 
1.652 
1.645 

1.638 

Inches. 
3.917 
3.905 
3.892 
3.879 
3.867 
3.854 

3.841 
3.828 
3.815 
3.803 
3.790 
3.777 

3.764 
3.750 
3.737 
3.724 
3.711 
3.698 

3.685 
3.672 
3.658 
3.645 
3.632 
3.618 

3.605 
3.592 
3.578 
3.565 
3.551 
3.538 

3.524 
3.511 
3.497 
3.483 
3.470 
3.456 

3.442 
3.429 
3.415 
3.401 
3.387 
3.373 

3.359 
3.345 
3.331 
3.317 
3.303 
3.289 

3.275 

Inches. 
5.876 
5.857 
5.838 
5.819 
5.800 
5.781 

5.762 
5.743 
5.723 
5.704 
5.684 
5.665 

5.646 
5.626 
5.606 
5.587 
5.567 
5.547 

5.528 
5.507 
5.488 
5.468 
5.448 
5.428 

5.408 
5.388 
5.367 
5.347 
5.327 
5.307 

5.287 
5.266 
5.  246 
5.225 
5.205 
5.184 

5.164 
5.143 
5.122 
5.101 
5.080 
5.060 

5.039 
5.018 
4.997 
4.976 
4.955 
4.934 

4.913 

Inches. 
7.835 
7.810 
7.784 
7.759 
7.733 
7.708 

7.682 
7.657 
7.631 
7.605 
7.579 
7.553 

7.527 
7.501 
7.475 
7.449 
7.422 
7.396 

7.370 
7.343 
7.317 
7.290 
7.264 
7.237 

7.210 

7.184 
7.156 
7.130 
7,103 
7.076 

7.049 
7.022 
6.994 
6.967 
6.940 
6.  912 

6.885 
6.857 
6.830 
6.802 
6.774 
6.746 

6.713 
6.691 
6.663 
6.635 
6.607 
6.579 

6.551 

Inches. 
9.794 
9.762 
9.730 
9.699 
9.667 
9.635 

9.603 
9.571 
9.539 
9.507 
9.474 
9.442 

9.409 
9.376 
9.344 
9.311 
9.278 
9.245 

9.212 
9.179 
9.146 
9.113 
9.080 
9.046 

,9.013 

8.980 
8.946 
8.  912 
8.878 
8.844 

8.811 

8.777 
8.742 
8.708 
8.674 
8.640 

8.606 
8.572 
8.537 
8.502 
8.468 
8.433 

8.398 
8.364 
8.328 
8.294 
8.258 
8.224 

8.188 

Inches. 
11.  752 
11.  714 
11.677 
11.638 
11.600 
11.562 

11.523 
11.485 
11.  446 
11.  408 
11.369 
11.330 

11.  291 
11.251 
11.212 
11.  173 
11.134 
11.094 

11.055 
11.015 
10.  975 
10.936 
10.  895 
10.855 

10.  816 
10.775 
10.  734 
10.  694 
10.654 
10.  613 

10.  573 
10.  532 
10.491 
10.450 
10.  409 
10.368 

10.  327 
10.286 
10.  244 
10.  202 
10.  161 
10.  120 

10.  078 
10.  036 
9.994 
9.952 
9.910 
9.868 

9.826 

Longi- 
tude 
inter- 
val. 

48° 

49° 

5.837 
11.  674 
17.511 
23.348 
29.185 

5 
10 
16 
20 
25 
30 

Inches. 
0.001 
.004 
.010 
.017 
.026 
.038 

Inches. 
0.001 
.004 
.010 
.017 
.026 
.038 

5.838 
11.  676 
17.  514 
23.352 

29.  190 

50° 

51° 

5.839 
11.  678 
17.  517 

•2:',.  :tv, 
29.  194 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.017 
.026 
.038 

0.001 
.004 
.009 
.017 
.026 
.037 

5.840 
11.  680 
17.520 
23.360 
29.200 

52° 

53° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.017 
.026 
.037 

0.001 
.004 
.009 
.016 
-.026 
.037 

5.841 
11.682 
17.523 
23.364 
29.204 

5.842 
11.684 
17.  526 
23.368 
29.210 

54° 

55° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.016 
.025 
.036 

0.001 
.004 
.009 
.016 
.025 
.036 

5.843 
11.686 
17.529 
23.372 
29.214 

56° 

5.844 
11.688 
17.532 
23.376 
29.220 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.016 
.025 
.036 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  6. — Coordinates  for  projection  of  maps  (scale  y^V^o  )• — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o        / 
56    00 
10 
20 
30 
40 
50 

67    00 
10 
20 
30 
40 
50 

58    00 
10 
20 
30 
40 
50 

59    CO 
10 
20 

30 
40 

50 

60    00 
10 
20 
30 
40 
50 

61     00 
10 
20 
30 
40 
50 

62    00 
10 
20 
30 
40 
50 

63    00 
10 
20 
30 
40 
50 

64    00 

Inches. 

Indies. 
1.638 
1.631 
1.624 
1.616 
1.609 
1.602 

1.595 
1.588 
1.581 
1.574 
1.566 
1.559 

1.552 
1.545 
1.538 
1.530 
"  1.523 
1.516 

1.509 
1.501 
1.494 

1.487 
1.479 
1.472 

1.465 
1.457 
1.450 
1.442 
1.435 
1.  428 

1.320 
1.313 
1.405 
1.398 
1.390 
1.383 

1.  375 

1.368 
1.360 
1.353 
1.345 
1.338 

1.330 
1.322 
1.315 
1.307 
1.300 
1.292 

1.284 

Inches. 
3.275 
3.261 
3.  247 
3.233 
3.219 
3.204 

3.190 
3.176 
3.162 
3.147 
3.133 
3.119 

3.104 
3.090 
3.  075  . 
3.061 
3,046 
3.032 

3.017 
3.003 
2.988 
2.  973 
2.959 
2.944 

2.  929 
2.  914 
2.900 
2:885 
2.870 
2.855 

2.840 
2.  825 
2.810 
2.795 
2.781 
2.766 

2.751 
2.736 
2.  720 
2.705 
2.690 
2.675 

2.660 
2.645 
2.630 
2.614 
2.599 
2.584 

2.569 

Inches. 
4.913 

4.892 
4.870 
4.849 
4.828 
4.807 

4.785 
4.764 
4.742 
4.721 
4.699 
4.678 

4.656 
4.634 
4.613 
4.591 
4.569 
4.547 

4.526 
4.504 
4.482 
4.460 
4.438 
4.416 

4.394 
4.  372 
4.349 
4.  327 
4.305 
4.283 

4.261 
4.238 
4.216 
4.193 
4.171 
4.148 

4.126 
4.103 
4.081 
4.058 
4.035 
4.013 

3.990 
3.967 
3.944 
3.921 
3.899 
3.876 

3.853 

Inches. 
6.551 
6.522 
6.494 
6.466 
6.437 
6.409 

6.380 
6.352 
6.323 
6.294 
6.266 
6.237 

6.208 
6.179 
6.150 
6.122 
6.092 
6.063 

6.034 
6.005 
5.976 
5.946 
5.917 
5.888 

5.858 
5.  829 
5.799 
5.770 
5.740 
5.710 

5.681 
5.651 
5.621 
5.591 
5.561 
5.531 

5.501 
5.471 
5.441 
5.410 
5.380 
5.350 

5.320 
5.290 
5.259 
5.228 
5.198 
5.168 

5.137 

Inches. 
8.188 
8.153 
8.118 
8.082 
8.046 
8.011 

7.976 
7.940 
7.904 
7.868 
7.832 
7.796 

7.760 
7.724 
7.688 
7.  -52 
7.  616 
7.579 

7.543 

7.506 
7.470 
7.433 
7.396 
7.360 

7.323 

7.286 
7.249 
7.212 
7.  175 
7.138 

7.101 

7.064 
7.026 
6.988 
6.952 
6.914 

6.877 
6.839 
6.801 
6.763 
6.726 
6.688 

6.650 
6.612 
6.574 
6.536 
6.498 
6.460 

6.422 

Inches. 
9.826 
9.784 
9.741 
9.698 
9.656 
9.613 

9.571 
9.  527 
9.485 
9.442 
9.398 
9.356 

9.313 
9.  269 
9.226 
9.182 
9.139 
9.095 

9.  052 

9.008 
8.963 
8.920 
8.876 
8.831 

8.788 
8.743 
8.699 
8.654 
8.610 
8.566 

8.  521 
8.476 
8.431 
8.386 
8.  342 
8.297 

8.252 
8.207 
8.161 
8.116 
8.071 
8.026 

7.980 
7.934 
7.889 
7.843 
7.797 
7.751 

7.706 

Longi- 
tude 
inter- 
val. 

56° 

57° 

5.845 
11.690 
17.535 
23.380 
29.  224 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.004 
.009 
.016 
.025 
.036 

Indies. 
0.001 
.001 
.009 
.016 
.024 
.035 

5.846 
11.692 
17.  537 
23.  383 
29.229 

58° 

59° 

5.847 
11.  694 
17.  540 
•   23.387 
29.  234 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.015 
.024 
.034 

0.001 
.004 
.008 
.015 
.024 
.034 

5.848 
11.  695 
17.543 
23.  391 
29.  238 

""5."  849" 
11.  697 
17.546 
23.  394 
29.  243 

60° 

61° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.008 
.015 
.023 
.033 

0.001 
.004 
.008 
.014 
.023 
.033 

5.850 
11.699 
17.549 
23.  398 
29.  248 

5 
10 
15 
20 
25 
30 

62° 

63° 

0.001 
.004 
.008 
.014 
.022 
.032 

0.001 
.003 
.008 
.014 
.022 
.031 

5.850 
11.  701 
17.  551 
23.  402 
29.  252 

64° 

5.851 
11.702 
17.554 
23.  405 
29.256 

5 
10 
15 
20 
25 
30 

O.OC1 
.OC. 
.008 
.013 
.021 
'     .030 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  6. — Coordinates  for  projection  of  maps  (scale  yWinnr) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


57 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

O          1 

64    00 
10 
20 
30 
40 
50 

65    00 
10 
20 
30 
40 
50 

66    00 
10 
20 
30 
40 
50 

67    00 
10 
20 
30 
40 
50 

68    00 
10 
.    20 
30 
40 
50 

69    00 
10 
20 
30 
40 
50 

70    00 
10 
20 
30 
40 
50 

71    00 
10 
20 
30 
40 
50 

72    00 

Inches. 

Inches. 
.284 
.277 
.269 
.261 
.254 
.246 

.238 
.231 
.223 
.215 
.207 
.200 

1.192 
1.184 
1.176 
1.168 
1.161 
1.153 

1.145 
1.137 
1.129 
1.121 
1.113 
1.106 

1.098 
1.090 
1.082 
1.074 
1.066 
1.058 

1.050 
1.042 
1.034 
1.026 
1.018 
1.010 

1.002 
.994 
.986 
.978 
.970 
.962 

.954 
.946 
.938 
.930 
.922 
.914 

.906 

Inches. 
2.569 
2.553 
2.538 
2.523 
2.507 
2.492 

2.477 
2.461 
2.446 
2.430 
2.415 
2.399 

2.384 
2.368 
2.352 
2.337 
2.321 
2.305 

2.290 
2.274 
2.258 
2.243 
2.227 
2.211 

2.195 
2.180 
2.164 
2.148 
2.132 
2.116 

2.100 
2.084 
2.068 
2.052 
2.037 
2.021 

2.005 
1.989 
.972 
.956 
.940 
.924 

.908 
.892 
.876 
.860 
.844 
1.828 

1.811 

Inches. 
3.853 
3.830 
3.807 
3.784 
3.761 
3.738 

3.715 
3.692 
3.668 
3.645 
3.  622 
3.599 

3.575 
3.552 
3.529 
3.505 
3.482 
3.458 

3.435 
3.411 
3.388 
3.364 
3.340 
3.317 

3.293 
3.269 
3.246 
3.222 
3.198 
3.174 

3.151 
3.127 
3.103 
3.079 
3.055 
3.031 

3.007 
2.983 
2.959 
2.935 
2.911 
2.886 

2.862 
2.838 
2.  814 
2.790 
2.765 
2.741 

2.717 

Inches. 
5.137 
5.106 
5.076 
5.045 
5.014 
4.984 

4.953 
4.922 
4.891 
4.860 
4.829 
4.798 

4.767 
4.736 
4.705 
4.673 
4.642 
4.611 

4.580 
4.548 
4.517 
4.485 
4.454 
4.422 

4.391 
4.359 
4.328 
4.296 
4.264 
4.232 

4.201 
4.169 
4.137 
4.105 
4.073 
4.041 

4.009 
3.977 
3.945 
3.913 
3.881 
3.848 

3.816 
3.784 
3.752 
3.720 
3.687 
3.655 

3.623 

Inches. 
6.422 
6.383 
6.345 
6.307 
6.268 
6.230 

.6.192 
6.153 
6.114 
6.075 
6.037 
5.998 

5.959 
5.920 
5.881 
5.842 
5.803 
5.764 

5.725 
5.685 
5.646 
5.607 
5.567 
5.528 

5.489 
5.449 
5.410 
5.370 
5.330 
5.291 

5.251 
5.211 
5.171 
5.131 
5.092 
5.052 

5.012 
4.  972 
4.931 
4.891 
4.851 
4.811 

4.771 
4.730 
4.690 
4.650 
4.609 
4.569 

4.529 

Inches. 
7.706 
7.660 
7.614 
7.568 
.7.  522 
7.476 

7.430 
7.384 
7.337 
7.290 
7.244 
7.198 

7.151 
7.104 
7.057 
7.010 
6.963 
6.916 

6.869 
6.  822 
6.775 
6.728 
6.680 
6.634 

6.586 
6.539 
6.491 
6.443 
6.396 
6.349 

6.301 
6.253 
6.205 
6.157 
6.110 
6.062 

6.014 
5.  966 
5.917 
5.  869 
5.  821 
5.773 

5.725 
5.676 
5.628 
5.579 
5.531 
5.483 

5.434 

Longi- 
tude 
inter- 
val. 

64° 

65° 

5.852 
11.704 
17.556 
23.408 
29.260 

"~5."  853" 
11.706 
•     17.558 
23.411 
29.264 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.003 
.008 
.013 
.021 
.030 

Inches. 
0.001 
.003 
.007 
.013 
.020 
.029 

66° 

67° 

5.854 
11.707 
17.561 
23.414 
29.268 

5 
10 
15 
20 
25 
v30 

0.001 
.003 
.007 
.013 
.020 
.029 

0.001 
.003 
.007 
.012 
.019 
.028 

5.854 
11.709 
17.563 
23.418 
29.272 

68° 

69° 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.007 
.012 
.019 
.027 

0.001 
.003 
.006 
.011 
.018 
.026 

5.855 
11.710 
17.565 
23.420 
29.276 

5.856 
11.712 
17.567 
23.423 
29.279 

70° 

71° 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.006 
.011 
.017 
.024 

0.001 
.003 
.006 
.010 
.016 
.024 

5.856 
11.  713 
17.  570 
23.426 
29.282 

"~5.~  857" 
11.  714 
17.572 
23.429 
29.286 

72° 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.006 
.010 
.016 
.023 

58 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  6. — Coordinates  for  projection  of  maps  (scale  T^V^o) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

~1 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o      / 
72    00 
10 
20 
30 
40 
50 

73    00 
10 
20 
30 
40 
50 

74    00 
10 
20 
30 
40 
50 

75    00 
10 
20 
30 
40 
50 

76    00 
10 
20 
30 
40 
50 

77    00 
10 
20 
30 
40 
50 

78    00 
10 
20 
30 
40 
50 

79    00 
10 
20 
30 
40 
50 

80    00 

Inches. 

Inches. 
.906 

.898 
.889 
.881 
.873 
.865 

.857 
.849 
.841 
.832 
.824 
.816 

.808 
.800 
.791 
.783 
.775 
.767 

.759 
.750 
.742 
.734 
.726 
.717 

.709 
.701 
.692 
.684 
.676 
.668 

.659 
.651 
.643 
.634 
.626 
.618 

.609 
.601 
.593 
.584 
.576 
.568 

.559 
.551 
.542 
.534 
.526 
.517 

.509 

Inches. 
1.811 
1.795 
1.779 
1.763 
1.746 
1.730 

1.714 

1.697 
1.681 
1.665 
1.648 
1.632 

1.616 
1.599 
1.583 
1.566 
1.550 
1.534 

£"517 
1.501 
1.484 
1.468 
1.451 
1.435 

1.418 
1.402 
1.385 
1.368 
1.352 
1.335 

1.319 

1.302 
1.285 
1.269 
1.  252 
1.235 

1.219 
1.202 
1.185 
1.169 
1.152 
1.  135 

1.119 
1.102 
1.085 
1.068 
1.052 
1.035 

1.018 

Inches. 
2.  717 
2.G93 
2.668 
2.644 
2.620 
2.595 

2.571 
2.546 
2.  522 
2.  497 
2.  473 
2.  448 

2.424 
2.  399 
2.374 
2.350 
2.325 
2.300 

2.276 
2.251 
2.226 
2.201 
2.177 
2.152 

2.127 
2.  102 
2.078 
2.053 
2.  028 
2.003 

1.978 
1.953 
1.928 
1.903 
1.878 
1.853 

1.828 
1.803 
1.778 
1.753 
1.728 
1.703 

1.678 
1.653 
1.628 
1.602 
1.577 
1.552 

1.527 

Inches. 
3.623 
3.590 
3.  558 
3.525 
3.493 
3.460 

3.428 
3.395 
3.  362 
3.330 
3.  297 
3.264 

3.232 
3.199 
3.160 
3.133 
3.100 
3.067 

3.034 
3.002 
2.  968 
2.935 
2.902 
2.870 

2.836 
2.803 
2.770 
2.  737 
2.704 
2.671 

2.638 
2.  604 
2.  571 
2.  538 
2.504 
2.471 

2.438 
2.404 
2.371 
2.338 
2.304 
2.270 

2.237 
2.  204 
2.170 
2.  136 
2.  103 
2.070 

2.036 

Inches. 
4.  529 
4.488 
4.447 
4.407 
4.366 
4.325 

4.285 
4.  244 
4.203 
4.162 
4.121 
4.081 

4.040 
3.999 
3.957 
3.916 
3.875 
3.834 

3.793 
3.752 
3.711 
3.669 
3.628 
3.587 

3.546 
3.504 
3.463 
3.  421 
3.380 
3.339 

3.297 
3.256 
3.214 
3.172 
3.131 
3.089 

3.047 
3.005 
2.964 
2.922 
2.880 
2.838 

2.797 
2.755 
2.713 
2.671 
2.629 
2.587 

2.  £45 

Inches. 
5.434 
5.386 
5.336 
5.  288 
5.239 
5.190 

5.141 
5.  092 
5.044 
4.994 
4.  94.) 
4.897 

4.847 
4.798 
4.748 
4.  699 
4.650 
4.601 

4.552 
4.502 
4.453 
4.403 
4.354 
4.304 

4.255 
4.  205 
4.155 
4.105 
4.056 
4.006 

3.956 
3.907 
3.856 
3.806 
3.757 
3.706 

3.656 
3.606 
3.556 
3.506 
3.456 
3.406 

3.356 
3.305 
3.255 
3.  205 
3.155 
3.104 

3.054 

Longi- 
tude 
inter- 
val. 

72° 

73° 

5.858 
11.  716 
17.  573 
23.  431 
29.289 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.003 
.006 
.010 
.016 
.023 

Inches. 
0.001 
.002 
.005 
.010 
.015 
.021 

5.858 
11.  717 
17.  575 
23.434 
29.  292 

5.859 
11.718 
17.  577 
23.  436 
29.  295 

74° 

75° 

5 
10 
15 
20 
25 
30 

0.001 
.002 
.005 
.009 
.014 
.020 

0.001 
.002 
.005 
.009 
.013 
.019 

5.860 
11.719 
17.  578 
23.  438 
29.  298 

5.860 
11.  720 
17.  580 
23.440 
29.300 

76° 

77° 

5 
10 
15 
20 
25 
30 

0.001 
.002 
.005 
.008 
.013 
.018 

0.000 
.002 
.004 
.007 
.012 
.017 

5.860 
11.721 
17.  582 
23.  442 
29.  302 

""s.'sei" 

11.  722 
17.583 
23.  444 
29.304 

""s.'sei" 

11.  723 
17.584 
23.  445 
29.306 

78° 

79° 

5 
10 
15 
20 
25 
30 

0.000 
.002 
.004 
.007 
.011 
.016 

0.000 
.002 
.004 
.006 
.010 
.014 

GEOGRAPHIC    TABLES    AND   FORMULAS. 


59 


TABLE  7. — Coordinates  for  projection  of  maps  (scale 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. - 

25'  longi- 
tude. 

30'  longi- 
tude. 

o      / 
0    00 

10 
20 
30 
40 

50 

1    00 

10 
20 
30 
40 
50 

2    00 

10 
20 
30 
40 
50 

3    00 

10 
20 
30 
40 
50 

4    00 

10 
20 
30 
40 
50 

5    00 

10 
20 
30 
40 

50 

6    00 

10 
20 
30 

40 
50 

7    00 

Inches. 

Inches. 
5.704 

5.764 
5.764 
5.764' 
5.764 
5.764 

5.764 

5.763 
5.763 
5.762 
5.762 
5.761 

5.761 

5.760 
5.759 
5.759 
5.758 
5.757 

5.756 

5.756 
5.754 
5.  753 
5.752 
5.751 

5.750 

5.749 
5.748 
5.746 
5.745 
5.744 

5.743 

5.741 
5.739 
4     5.738 
5.736 
5.735 

5.733 

5.  731 
5.729 
5.727 
5.726 
5.724 

5.  722 

Inches. 
11.  529 

11.  528 
11.  528 
11.  528 
11.528 
11.  527 

11.  527* 

11.  526 
11.525 
11.524 
11.  524 
11.523 

11.  522 

11.  520 
11.  519 
11.517 
11.516 
11.  514 

11.513 

11.511 
11.509 
11.507 
11.505 
11.503 

11.501 

11.  498 
11,4% 
11.493 
11.490 

11.488 

11.485 

11.482 
11.479 
11.476 
11.472 
11.  469 

11.466 

11.462 
11.458 
11.455 
11.451 
11.  447 

11.443 

Inches. 
17.  293 

17.  293 
17.  292 
17.  292 
17.  291 
17.  291 

17.291 

17.  289 
17.  288 
17.287 
17.  285 
17.  284 

17.283 

17.  281 
17.  278 
17.276 
17.  274 
17.  272 

17.  270 

17.  267 
17.264 
17.  260 
17.  257 
17.254 

17.  251 

17.  247 
17.  243 
17.  240 
17.  236 
17.  232 

17.  228 

17.  223 
17.218 
17.  213 
17.209 
17.  204 

17.  199 

17.  193 
17.  188 
17.  182 
17.  177 
17.  171 

17.165 

Inches. 
23.058 

23.  057 
23.056 
23.  056 
23.  055 
23.054 

23.054 

23.  052 
23.050 
23.049 
23.047 
23.  045 

23.044 

23.041 
23.038 
23.035 
23.  032 
23.  029 

23.026 

23.  022 
23.  018 
23.014 
23.  010 
23.006 

23.002 

22.  996 
22.  991 
22.986 
22.  981 
22.  976 

22.  970 

22.964 
22.  958 
22.  951 
22.945 
22.  938 

22.932 

22.924 
22.917 
22.910 
22.  902 
22.  894 

22.  887 

Inches. 
28.  822 

28.  821 
28.  821 
28.  820 
28.  819 
28.818 

28.818 

28.816 
28.  813 
28.811 
28.  809 
28.807 

28.  805 

28.  801 
28.797 
28.  794 
28.  790 
28.  786 

28.  783 

28.  778 
28.  773 
28.  767 
28.  762 
28.  757 

28.  752 

28.  746 
28.739 
28.  733 
28.  726 
28.  720 

28.  7l3 

28.  705 
28.  697 
28.  689 
28.  681 
28.  673 

28.  665 

28.  656 
28.  646 
28.  637 
28.628 
28.  618 

28.  609 

Inches. 
34.586 

34.585 
34.  585 
34.  583 
34.583 
34.  582 

34.581 

34.  579 
34.576 
34.573 
34.571 
34.568 

34.565 

34.561 
34.  556 
34.552 
34.  548 
34.543 

34.539 

34.533 
34.527 
34.520 
34.  514 
34.  508 

34.502 

34.  495 
34.  487 
34.  479 
34.  471 
34.  463 

34.  456 

34.  446 
34.  436 
34.  427 
34.  417 
34.  408 

34.398 

34.387 
34.  375 
34.364 
34.  353 
34.342 

34.330 

Longi- 
tude 
inter- 
val. 

0° 

1° 

11.  451 
22.  901 
34.352 
45.803 
57.254 

68.704 

11.  451 
22.  901 
34.352 
45.803 
57.254 

08.  704 

11.451 
22.902 
34.353 
45.804 
57.254 

68.705 

5 
10 
15 
20 
25 
30 

Inch. 
0.000 
.000 
.000 
.000 
.000 
.000 

Inch. 
0.000 
.000 
.001 
.001 
.002 
.003 

2° 

3° 

5 
10 
15 
20 
25 
30 

0.000 
.001 
.001 
.002 
.004 
.005 

0.000 
.001 
.002 
.003 
.005 
,098 

11.  451 

22.902 
34.353 
45.804 
57.  255 

68.706 

4° 

5° 

11.  451 
22.903 
34.354 
45.805 
57.256 

68.708 

5 

10 
15 
20 

25 
30 

0.000 
.001 
.OJ3 
.005 
.007 
.011 

0.000 
.001 
.003 
.006 
.009 
.013 

11.452 
22.903 
34.855 
45.806 
57.258 

68.  710 

6° 

7° 

5 
10 
15 
20 
25 
30 

0.000 
.002 
.004 
.007 
.011 
.016 

0.000 
.002 
.005 
.008 
.013 
.018 

11.  452 
22.904 
34.356 

45.808 
57.260 

68.712 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE?. — Coordinates  for  projection  of  maps  (scale  ^3^7) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

O         ' 

1    00 

10 
20 
30 
40 
50 

8    00 

10 
20 
30 
40 
50 

9    00 

10 
20 
30 
40 
50 

10    00 

10 
20 
30 
40 
50 

11     00 

10 
20 
30 
40 
50 

12    00 

10 
20 
30 
40 
50 

13    00 

10 
20 
30 
40 
50 

14    00 

Inches. 
68.  712 

Inches. 

5.722 

5.720 
5.717 
5.715 
5.713 
5.711 

5.709 

5.706 
5.704 
5.701 
5.699 
5.696 

5.694 

5.691 
5.688 
5.686 
5.  683 
5.680 

5.677 

5.674 
5.671 
5.668 
5.665 
5.662 

5.659 

5.656 
5.652 
5.  649 
5.646 
5.642 

5.639 

5.636 
5.632 
5.628 
5.625 
5.  621 

5.618 

5.614 
5.610 
5.606 
5.602 
5.598 

5.594 

Inches. 
11.443 

11.439 
11.435 
11.430 
11.426 
11.  422 

11.417 

11.412 
11.407 
11.403 
11.  398 
11.  393 

11.388 

11.382 
11.  377 
11.371 
11.  366 
11.360 

11.355 

11.349 
11.343 
11.337 
11.331 
11.324 

11.318 

11.312 
11.305 
11.298 
11.292 
11.285 

11.  278 

11.271 
11.  264 
11.257 
11.250 
11.  242 

11.235 

11.  227 
11.220 
11.212 
11.204 
11.  196 

11.188 

Inches. 
17.  165 

17.  159 
17.  152 
17.  146 
17.139 
17.  132 

17.  126 

17.  119 
17.111 
17.104 
17.096 
17.089 

17.082 

17.  073 
17.065 
17.057 
17.049 
17.040 

17.  032 

17.  023 
17.  014 
17.005 
16.996 
16.987 

16.978 

16.968 
16.958 
16.  948 
16.938 
16.928 

•  16.918 

16.  907 
16.  896 
16.885 
16.874 
16.864 

16.853 

16.  841 
16.  829 
16.  818 
16.806 
16.  794 

16.783 

Inches. 

22.887 

22.  878 
22.  869 
22.  861 
22.  852 
22.  843 

22.834 

22.825 
22.  815 
22.805 
22.795 
22.786 

22.776 

22.764 
22.754 
22.  742 
22.732 
22.  720 

22.  710 

22.698 
22.  685 
22.673 
22.  661 
22.649 

22.  637 

22.  624 
22.610 
22.  597 
22.584 
22.570 

22.  557 

22.5*42 
22.  528 
22.  514 
22.  499 
.22.485 

22.  470 

22.455 
22.  439 
22.  424 
22.  408 
22.392 

22.377 

Inches. 
28.609 

28.  598 
28.587 
28.  576 
28.565 
28.554 

28.543 

28.531 
28.  519 
28.  507 
28.494 

28.  482 

•  28.  470 

28.456 
28.  442 
28.428 
28.415 
28.  401 

28.387 

28.372 
28.  357 
28.342 
28.327 
28.  311 

28.  296 

28.280 
28.  263 
28.  246 
28.230 
28.  213 

28.  196 

28.  178 
28.  160 
28.  142 
28.  124 
28.106 

28.088 

28.069 
28.  049 
28.030 
28.  010 
27.  991 

27.  971 

Incites. 
34.  330 

34.  317 
34.  304 
34.  291 
34.  278 
34.265 

34.252 

34.237 
34.  222 
34.208 
34.193 
34.  178 

34.163 

34.147 
34.130 
34.  114 
34.  097 
34.  081 

34.064 

34.046 
34.  028 
34.  010 
33.  992 
33.973 

33.955 

"33.935 
33.915 
33.895 
33.875 
33.855 

33.835 

33.814 
33.  792 
33.770 
33.  749 

33.  727 

33.  706 

33.682 
33.  659 
33.635 
'  33.612 
33.589 

33.565 

Longi- 
tude 
inter- 
val. 

7° 

8° 

11.452 
22.905 
34.358 
45.  810 
57.  262 

68.715 

5 
10 
15 
20 
25 
30 

Inch. 

0.000 
.002 
005 
.008 
.013 
.018 

Inch. 
0.001 
.002 
.005 
.009 
.014 
.021 

11.  453 
22.906 
34.359 
45.  812 
57.265 

68.718 

9° 

10° 

11.454 
22.907 
33.361 
45.  814 
57.268 

68.722 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.006 
.010 
.016 
.023 

0.001 
.003 
.006 
.011 
.018 
.026 

11.  454 
22.909 
34.263 

45.817 
57.  272 

68.726 

11° 

12° 

11.455 
22.  910 
34.365 
45.820 
57.275 

68.730 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.007 
.013 
.020 
.028 

0.001 
.003 
.008 
.014 
.021 
.031 

11.456 
22.  912 
34.  367 
45.823 
57.279 

68.735 

13° 

14° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.008 
.015 
.023 
.033 

0.001 
.004 
.009 
.016 
.025 
.035 

11.457 
22.913 
34.370 
45.  827 
57.284 

68.740 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


61 


TABLE  7.  —  Coordinates  for  projection  of  maps  (scale 

[From  Smithsonian  Geographical  Tables.] 


—  Continued. 


Lati- 
tude of 

parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

O          ' 

14    00 

10 

20 
30 
40 
50 

15    00 

10 
20 
30 

40 
50 

16    00 

10 
20 
30 

w 

50 
17    00 

10 
20 
30 
40 
50 

18    00 

10 
20 
30 
40 
50 

19    00 

10 
20 
30 
40 

50 

20    00 

10 
20 
30 
40 
50 

21    00 

9 

Inches. 
68.740 

Inches. 
5.594 

6.590 
5.586 
5.582 
5.578 
5.573 

5.569 

5.565 
5.560 
5.556 
5.551 
5.547 

5.542 

5.538 
5.533 
5.528 
5.524 
5.519 

5.514 

5.509 
5.504 
5-499 
o7494 
5.489 

5.484 

5.479 
5.473 
5.468 
5.463 
5.458 

5.452 

5.447 
5.441 
5.436 
5.430 
5.424 

5.419 

5.413 

5.407 
5.401 
5.396 
5.390 

5.384 

Inches. 
11.188 

11.180 
11.  172 
11.  163 
11.155 
11.147 

11.138 

11.130 
11.  121 
11.  112 
11.103 
11.094 

11.085 

11.076 
11.066 
11.057 
11.047 
11.038 

11.028 

11.018 
11.008 
10.998 
10.988 
10.  978 

10.968 

10.  957 
10.947 
10.936 
10.  926 
10.  915 

10.905 

10.893 
10.882 
10.  871 
10.860 
10.849 

10.838 

10.  826 
10.  814 
10.803 
10.  791 
10.  779 

10.768 

Inches. 
16.  783 

16.  770 
16.758 
16.  745 
16.733 
16.  720 

16.708 

16.694 
16.681 
16.667 
16.654 
16.  641 

16.628 

16.  613 
16.599 
16.585 
16.  571 
16.556 

16.542 

16.  527 
16.  512 
16.497 
16.  482 
16.  467 

16.452 

16.436 
16.  420 
16.  404 
16.389 
16.  373 

16.357 

16.  340 
16.  324 
16.  307 
16.  290 
16.274 

16.257 

16.  239 
16.222 
16.  204 
16.  187 
16.169 

16.  151 

Inches. 
22.377 

22.360 
22.344 
22.327 
22.  310 
22.294 

22.277 

22.259 
22.241 
22.223 
22.206 

22.188 

22.170 

22.151 
22.  132 
22.  113 
22.094 
22.075 

22.056 

22.036 
22.016 
21.996 
21.  976 
21.956 

21.936 

21.  915 
21.894 
21.  872 
21.852 
21.830 

21.809 

21.787 
21.  765 
21.  742 
21.  720 
21.  698 

21.  676 

21.652 
21.  629 
21.605 
21.  582 
21.558 

21.535 

Inches. 
27.  971 

27.950 
27.930 
27.909 
27.888 
27.867 

27.846 

27.  824 
27.802 
27.  779 
27.  757 
27.735 

27.713 

27.689 
27.665 
27.642 
27.  618 
27.594 

27.  571 

27.546 
27.521 
27.  495 
27.  470 
27.445 

27.420 

27.394 
27.367 
27.341 
27.  315 
27.288 

27.  262 

27.234 
27.  206 
27.178 
27.  150 
27.  123 

27.095 

27.065 
27.036 
27.007 
26.978 
26.  948 

26.  919 

Inches. 
33.565 

33.540 
33.515 
33.490 
33.465 
33.440 

33.415 

33.389 
33.  362 
33.335 
33.  308 
33.  282 

33.255 

33.227 
33.198 
33.170 
33.142 
33.113 

33.085 

33.055 
33.025 
32.994 
32.964 
32.  934 

32.904 

32.872 
32.840 
32.809 
32.  777 
32.  746 

32.  714 

32.680 
32.  647 
32.  614 
32.  580 
32.  547 

32.513 

32.  478 
32.443 
32.408 
32.  373 
32.338 

32.303 

Longi- 
tude 
inter- 
val. 

14° 

15° 

11.458 
22.915 
34.373 
45.830 

57.288 

68.746 

5 
10 
15 

"  20 

25 
30 

Inches. 
0.001 
.004 
.009 
.018 
.025 
.035 

Inches. 
0.001 
.004 
.009 
.017 
.026 
.038 

11.459 
22.917 
34.376 
45.834 
57.293 

68.752 

16° 

17° 

11.460 
22.919 
34.379 
45.838 
57.298 

68.758 

'       5 
10 
15 
20 
25 
30 

0.001 
.004 
.010 
.018 
.028 
.040 

0.001 
.005 
.011 
.019 
.029 
.042 

11.461 
22.921 
34.382 
45.843 
57.304 

68.764 

18° 

19° 

11.462 
22.924 
34.386 
45.848 
57.  310 

68:771 

5 
10 
15 
20 
25 
30 

0.001 
.005 
.T)ll 
.020 
.031 
.044 

0,001 
.005 
.012 
.021 
.032 
.046 

11.463 
22.926 
34.390 
45.853 
57.  316 

68.779 

20° 

21° 

5 
10 
15 
20 
25 
30 

0.001 
.005 
.012 
.022 
.034 
.049 

0.001 
.006 
.013 
.022 
.035 
.051 

11.464 
22.929 
34.394 

45.858 
57.322 

68.787 

02  aEOGKAPHIC    TABLES    AND    FOKMULA8. 

TABLE  7. — Coordinates  for  projection  of  maps  (scale  -$3^-3} — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o      / 
21    00 

10 
20 
30 
40 
50 

22    00 

10 
30 
30 
40 
50 

23    00 

10 
20 
30 
40 
50 

24    00 

10 
20 
30 
40 
50 

25    00 

10 
20 
30 
40 
50 

26    00 

10 
20 
30 
40 
50 

27    00 

10 
20 
30 
40 
50 

28    00 

Inches. 

68.  787 

Inches. 
5.384 

5.378 
5.372 
5.366 
5.359 
5.353 

.  5..347 

5.341 
5.334 

5.328 
5.322 
5.315 

5.309 

5.302 
5.296 
5.289 
5.  282 
5.276 

5.269 

5.  263 
5.256 
'   5.249 
5.  242 
5.235 

5.227 

5.220 
5.213 
5.206 
5.199 
5.191 

5.184 

'  5.  177 
5.169 
5.162 
5.154 
5.147 

5.140 

5.132 
5.124 
5.116 
5.109 
5.101 

5.093 

Inches. 
10.  768 

10.  755 
10.  743 
10.  731 
10.  719 
10.  707 

10.  694 

10.682 
10.  669 
10.  656 
10.  643 
10.  631 

10.618 

10.604 
10.  591 
10.  578 
10.565 
10.551 

10.  538 

10.  526 
10.  512 
10.  498 
10.  483 
10.  469 

10.  455 

10.  441 
10.  426 
10.  412 
10.  397 
10.383 

10.369 

10.354 
10.  339 
10.  324 
10.309 
10.294 

10.279 

10.264 
10.  248 
10.233 
10.  218 
10.202 

10.  187 

Inches. 
16.  151 

16.  133 
16.115 
16.097 
16.  078 
16.  060 

16.042 

16.  022 
16.003 
15.984 
15.  965 
15.  946 

15.927 

15.907 
15.  887 
15.  867 
15.  847 
15.  827 

15.807 

15.  789 
15.  767 
15.  74fi 
15.  725 
15.  704 

15.  682 

15.661 
15.639 
15.  618 
15.  596 
15.  575 

15.553 

15.531 
15.508 
15.  486 
15.  463 
15.  441 

15.  419 

15.  396 
15.  373 
15.  349 
15.  326 
15.  303 

15.  280 

Inches. 
21.  535 

21.511 
21.486 
21.462 
21.438 
21.413 

21.  389 

21.  363 
21.338 
21.  312 
21.287 
21.  261 

21.  236 

21.  209 
21.  182 
21.156 
21.  129 
21.  102 

21.  076 

21.  052 
21.023 
20.  995 
20.  967 
20.  938 

20.  910 

20.881 
20.852 
20.  824 
20.  795 
20.  766 

20.  737 

20.  708 
20.  678 
20.  648 
20.  618 
20.  588 

20.  558 

20.  528 
20.  497 
20.  466 
20.  435 
20.  404 

20.  374 

Inches. 
26.  919 

26.889 
26.858 
26.  828 
26.  797 
26.  767 

26.736 

26.  704 
26.  672 
26.641 
26.  609 
26!577 

26.545 

26.  511 
26.  478 
26.  445 
26.  412 
26.  378 

26.345 

26.  315 
26.279 
26.  244 
26.209 
26.  173 

26.  137 

26.  101 
26.  065 
26.  029 
25.  993 
25.  958 

25.  922 

25.884 
25.847 
25.  810 
25.  772 
25.  735 

25.  698 

25.  659 
25.  621 
25.582 
25.544 
25.  505 

25.  467 

Inches. 
32.  303 

32.  566 
32.230 
32.  193 
32.  156 
32.  120 

32.  083 

32.  045 
82.  006 
31.  969 
31.930 
31.892 

31.853 

31.813 
31.  774 
31.733 
31.  694 
31.  654 

31.  614 

31.  577 
31.  535 
31.  493 
31.450 
31.408 

31.  365 

31.322 
31.  279 
31.235 
31.  192 
31.  149 

31.106 

31.061 
31.017 
30.  972 
30.  927 
30.  882 

30.838 

30.  791 
30.  745 
30.  699 
30.  653 
30.  607 

30.  560 

c 

Longi- 
tude 
inter- 
val. 

21° 

22° 

11.466 
22.  932 
34.  397 
45.  863 
57.329 

68.  795 

5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.006 
.013 
.022 
.035 
.051 

Inches. 
0.001 
.006 
.013 
.023 
.036 
.052 

11.  467 
22.  934 
34.  401 
45.  868 
57.  336 

68.803 

23° 

24° 

11.469 
22.937 
34.406 
45.  874 
57.  343 

68.  812 

5 

10 
15 
20 
25 
30 

0.001 
.006 
.014 
.024 
.038 
.054 

0.002 
.006 
.014 
.025 
.039 
.056 

11.470 
22.940 
34.  410 

45.880 
57.350 

68.'821 

25° 

26° 

5 
10 
15 
20 
25 
30 

0.002 
.006 
.014 
.026 
.040 
.058 

0.002 
.007 
.015 
.026 
.041 
.059 

11.  472 
22.  943 
34.  415 

45.886 
57.  358 

68.830 

11.  473 
22.946 
34.419 

If).  S'.fJ 

57.  365 
68.838 

27° 

28° 

5 
10 
15 
20 
25 
30 

0.002 
.007 
.015 
.027 
.042 
.061 

0.002 
.007 
.016 
.028 
.043 
.063 

11.  475 
22.950 
34.  424 
45.899 
57.  374 

68.849 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


63 


TABLE  7. — Coordinates  for  projection  of  maps  (scale  ^3^) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 

parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o      / 
28    00 

10 
20 
30 
40 
50 

29    00 

10 
20 
30 

40 
50 

30    00 

10 
20 

30 
40 
50 

31    00 

10 
20 
30 
40 
50 

32    00 

10 
20 
30 
40 
50 

33    00 

10 
20 
30 
40 
50 

3-1    00 

10 
20 
30 
40 
50 

35    00 

Inches. 
68.849 

Inches. 
5.093 

5.085 
5.077 
5.069 
5.061 
5.054 

5.046 

5.037 
5.029 
5.021 
5.013 
5.004 

4.996 

4.988 
4.979 
4.971 
4.962 
4.954 

4.945 

4.937 
4.928 
4.919 
4.910 
4.902 

4.  893 

4.884 
4.875 
4.866 
4.857 
4.848 

4.839 

4.830 
4.821 
4.812 
4.802 
4.793 

4.784 

4.774 
4.765 
4.755 
4.746 
4.737 

4.727 

Inches. 
10.  187 

10.  171 
10.  155 
10.  139 
10.  123 
10.  107 

10.091 

10.  075 
10.058 
10.042 
10.  025 
10.009 

9.993 

9.976 
9.959 
9.942 
9.925 
9.908 

9.891 

9.873 
9.856 
9.838 
9.821 
9.804 

9.786 

9.768 
9.750 
0.732 
9.714 
9.696 

9.679 

9.660 
9.642 
9.  623 
9.605 
9.586 

9.568 

9.549 
9.530 
9.  511 
9.492 
9.473 

9.454 

Inches. 
15.280 

15.  256 
15.232 
15.  208 
15.  185 
15.  161 

15.  137 

15.  112 
15.087 
15.063 
15.038 
15.  013 

14.  989 

14.963 
14.  938 
14.912 
14.887 
14.862 

14.836 

14.810 
14.784 
14.758 
14.  731 
14.  705 

14.  679 

14.652 
14.  625 
14.  598 
14.572 
14.545 

14.518 

14.490 
14.  462 
14.  435 
14.  407 
14.  379 

14.  352 

14.  323 
14.  295 
14.  267 
14.238 
14.210 

14.  181 

Inches. 
20.  374 

20.342 
20.  310 
20.  278 
20.  246 
20.  214 

20.  182 

20.  1-50 
20.117 
20.084 
20.  051 
20.  018 

19.985 

19.  951 
19.  917 
19.  883 
19.  849 
19.  815 

19.  782 

19.  747 
19.  712 
19.677 
19.642 
19.607 

19.  572 

19.536 
19.500 
19.  465 
19.429 
19.  393 

19.  357 

19.320 
19.  283 
19.  246 
19.  210 
19.173 

19.  136 

19.  098 
19.060 
19.022 
18.  984 
18.946 

18.908 

Inches. 
25.467 

25.  427 
25.387 
25.  347 
25.  308 
25.  268 

25.228 

25.  187 
25.146 
25.  105 
25.064 
25.022 

24.  981 

24.  939 
24.  896 
24.  854 
24.  812 
24.  769 

24.  727 

24.  683 
24.  640 
24.  596 
24.  552 
24.509 

24.465 

24.  420 
24.  376 
24.  331 
24.286 
24.  241 

24.  196 

24.150 
24.  104 
24.  058 
24.012 
23.966 

23.920 

23.  872 
23.  825 
23.  778 
23.  730 
23.  683 

23.  636 

Inches. 
30.560 

30.  513 
30.465 
30.  417 
30.  369 
30.321 

30.  274 

30.224 
30.  175 
30.  126 
30.076 
30.027 

29.  978 

29.  927 
29.  876 
29.825 
29.  774 
29.  723 

29.  672 

29.  620 
29.568 
29.515 
29.  463 
29.411 

29.358 

29.  305 
29.  251 
29.  197 
29.  143 
29.  089 

29.  036 

28.  980 
28.  925 
28.870 
28.814 
28.  759 

28.  704 

28.  647 
28.590 
28.  533 
28.  476 
28.420 

28.  363 

Longi- 
tude 
inter- 
val. 

28° 

29° 

11.  476 
22.953 
34.430 
45.906 
57.383 

68.859 

5 
10 
15 
20 
25 
30 

Inches. 
0.002 
.007 
.016 
.028 
.043 
.063 

Indies. 
0.002 
.007 
.016 
.028 
.044 
.064 

11.478 
22.  957 
34.435 
45.  913 
57.  391 

68.870 

30° 

31°   " 

11.480 
22.960 
34.  440 
45.920 
57.400 

68.880 

11.482 
22.964 
34.446 
45.927 
57.409 

68.891 

5 
10 
15 
20 
25 
30 

0.002 
.007 
.016 
.029 
.045 
.065 

0.002 
.007 
.017 
.030 
.046 
.067 

32° 

33° 

11.484 
22.967 
34.451 
45.  934 

57.418 

68.902 

11.  4a5 
22.  971 
34.456 
45.  942 
57.  427 

68.913 

5 
10 
15 
20 
25 
30 

0.002 
.007 
.017 
.030 
.047 
.068 

0.002 
.008 
.017 
.031 
.048 
.069 

34° 

35° 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.017 
.031 
.049 
.070 

0.002 
.008 
.018 
.031 
.049 
.071 

11.487 
22.  975 
34.462 
45.949 
57.437 

68.924 

64 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  7. — Coordinates  for  projection  of  maps  (scale  -$-3^-5) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o        / 
35    00 

10 
20 
30 
40 
50 

36    00 

10 
20 
30 

40 
50 

37    00 

10 
20 
30 
40 

50 

38    00 

10 
20 
30 
40 
50 

39    00 

10 
20 
30 
40 
50 

40    00 

10 
20 

30 
40 
50 

41    00 

10 
20 
30 
40 
50 

42    00 

Inches. 
68.  924 

Inches. 
4.727 

4.717 

4.708 
4.698 
4.688 
4.  679 

4.669 

4.659 
4.649 
4.639 
4.629 
4.619 

4.609 

4.599 
4.589 
4.579 

4.568 
4.558 

4.548 

4.538 
4.  527 
4.517 
4.506 
4.496 

4.486 

4.475 
4.464 
4.454 
4.443 
4.433 

-  4.'  422 

4.411 
4.400 
4.389 
4.378 
4.368 

4.357 

4.346 
4.335 
4.324 
4.312 
4.301 

4.290 

Inches. 
9.454 

9.435 
9.415 
9.396 
9.377 
9.357 

9.338 

9.318 
9.298 
9.278 
9.  258 
9.238 

9.219 

9.198 
9.178 
9.157 
9.137 
9.117 

9.096 

9.076 
9.055 
9.034 
9.013 
8.992 

8.971 

8.950 
8.929 
8.908 
8.886 
8.865 

8.844 

8.822 
8.800 
8.779 
8.757 
8.735 

8.713 

8.691 
8.669 
8.647 
8.625 
8.603 

8.581 

Inches. 
14.  181 

14.  152 
14.  123 
14.094 
14.065 
14.  036 

14.007 

13.  977 
13.  947 
13.917 
13.887 
13.858 

13.828 

13.  797 
13.  767 
13.  736 
13.  706 
13.  675 

13.645 

13.  613 
13.582 
13.  551 
13.520 
13.488 

13.457 

13.425 
13.  393 
13.361 
13.  330 
13.298 

13.266 

13.  233 
13.201 
13.168 
13.  135 
13.  103 

13.  070 

13.  037 
13.004 
12.  971 
12.  937 
12.904 

12.  871 

Inches. 
18.908 

18.  870 
18.  831 
•   18.792 
18.  753 
18.  714 

18.  676 

18.  636 
18.596 
18.556 
18.517 
18.  477 

18.  437 

18.  396 
18.356 
18.  315 
18.274 
18.234 

18.  193 

18.  151 
18.  109 
18.  068 
18.  026 
17.  984 

17.943 

17.900 
17.858 
17.815 
17.773 
17.  730 

17.688 

17.  644 
17.  601 
17.  557 
17.514 
17.470 

17.427 

17.  383 
17.  338 
17.294 
17.250 
17.  205 

17.  161 

Indies. 
23.  636 

23.  587 
23.  539 
23.490 
23.442 
23.  393 

23.345 

23.  295 
23.245 
23.  195 
23.146 
23.0% 

23.046 

22.995 
22.  944 
22.894 
22.843 
22.  792 

22.  741 

22.689 
22.  637 
22.585 
22.  533 
22.  481 

22.429 

22.375 
22.  322 
22.  269 
22.  216 
22.  163 

22.110 

22.055 
22.  001 
21.  947 
21.  892 
21.838 

21.  784 

21.  728 
21.  673 
21.618 
21.562 
21.507 

21.451 

Inches. 
28.363 

28.  305 
28.  246 
28.188 
28.130 
28.072 

28.  014 

27.954 
27.  894 
27.835 
27.  775 
27.  715 

27.656 

27.594 
27.  533 
27.472 
27.411 
27.350 

27.289 

27.227 
27.164 
27.  102 
27.  039 
26.  977 

26.  914 

26.851 
26.  787 
26.  723 
26.  659 
26.  595 

26.532 

26.  466 
26.401 
26.336 
26.  271 
26.  206 

26.  140 

26.  074 
26.007 
25.941 
25.  875 
25.  808 

25.  742 

Longi- 
tude 
inter- 
val. 

35° 

36° 

11.  489 
22.  978 
34.  468 
45.  957 
57.  446 

68.935 

5 
10 
15 
20 

25 
30 

Inches. 
0.002 
.008 
.018 
.031 
.049 
.071 

Inches. 
0.002 
.008 
.018 
.032 
.050 
.072 

11.491 
22.983 
34.474 
45.  965 
57.457 

68.948 

37° 

38° 

11.  493 

22.  986 
34.480 
45.973 
57.466 

68.  959 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.018 
.032 
.050 
.073 

0.002 
.008 
.018 
.033 
.051 
.073 

11.  495 
22.990 
34.485 
45.  980 
57.  475 

68.970 

39° 

40° 

11.497 
22.994 
34.  491 

45.988 
57.485 

68.  982 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.018 
.033 
.051 
.074 

0.002 
.008 
.019 
.033 
.052 
.074 

11.499 
22.998 
34.497 
45.996 
57.  495 

68.994 

41° 

42° 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.019 
.033 
.052 
.075 

0.002 
.008 
.019 
.033 
.052 
.075 

11.501 
23.002 
34.503 
46.004 
57.506 

69.007 

GEOGEAPHIC    TABLES    AND    FOEMULA8. 


65 


TABLE  7. — Coordinates  for  projection  of  maps  (scale  ro^nr) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

107  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 
42    00 

10 
20 
30 
40 
50 

43    00 

10 
20 
30 
40 
50 

44    00 

10 
20 
30 
40 
50 

45    00 

10 
20 
30 
40 
50 

46    00 

10 
20 
30 
40 
50 

47    00 

10 
20 
30 
40 
50 

48    OQ 

10 
20 
30 
40 
50 

49    00 

Inches. 
69.007 

Inches. 
4.290 

4.279 
4.268 
4.256 
4.245 
4.234 

4.222 

4.211 
4.199 
4.188 
4.176 
4.165 

4.153 

4.142 
4.130 
4.118 
4.106 
4.095 

4.083 

4.071 
4.059 
4.047 
4.035 
4.023 

4.011 

3.999 
3.987 
3.975 
3.963 
3.951 

3.938 

3.926 
3.914 
3.901 
3.889 
3.877 

3.864 

3.852 
3.839 
3.827 
3.814 
3.802 

3.789 

Inches. 
8.581 

8.558 
8.535 
8.513 
8.490 
8.467 

8.445 

8.422 
8.399 
8.376 
8.353 
8.330 

8.307 

8.283 
8.260 
8.236 
8.213 
8.189 

8.166 

8.142 
8.118 
8.094 
8.070 
8.046 

8.023 

7.998 
7.974 
7.950 
7.925 
7.901 

7.877 

7.852 
7.827 
7.803 
7.778 
7.753 

7.729 

7.704 
7.679 
7.653 
7.628 
7.603 

7.678 

Inches. 
12.  871 

12.837 
12.803 
12.769 
12.735 
12.  701 

12.667 

12.633 
12.  598 
12.564 
12.529 
12.  494 

12.460 

12.425 
12.390 
12.354 
12.319 
12.284 

12.  249 

12.  213 
12.  177 
12.  141 
12.  105 
12.  070 

12.034 

11.997 
11.961 
11.925 
11.888 
11.852 

11.  815 

11.  778 
11.  741 
11.704 
11.667 
11.630 

11.593 

11.555 
11.  518 
11.480 
11.442 
11.  405 

11.367 

Inches. 
17.  161 

17.  116 
17.  071 
17.  025 
16.980 
16.935 

16.890 

16.844 
16.  798 
16.  751 
16.  705 
16.  659 

16.  613 

16.566 
16.  519 
16.  473 
16.426 
16.  379 

16.332 

16.284 
16.236 
16.188 
16.  141 
16.093 

16.045 

15.997 
15.948 
15.899 
15.  851 
15.802 

15.754 

15.704 
15.655 
15.606 
15.556 
15.507 

15.457 

15.  407 
15.357 
15.307 
15.257 
15.206 

15.156 

Inches. 
21.  451 

21.395 
21.338 
21.  282 
21.225 
21.  169 

21.  112 

21.054 
20.997 
20.939 
20.882 
20.824 

20.767 

20.708 
20.649 
20.  591 
20.532 
20.473 

20.  415 

20.355 
20.295 
20.236 
20.  176 
20.  116 

20.056 

19.996 
19.  935 
19.  874 
19.  813 
19.  753 

19.692 

19.630 
19.569 
19.507 
19.445 
19.  383 

19.  322 

19.259 
19.196 
19.  134 
19.  071 
19.008 

18.945 

Inches. 
25.  742 

25.674 
25.606 
25.538 
25.  470 
25.402 

25.334 

25.265 
25.1% 
25.127 
25.058 
24.  989 

24.920 

24.849 
24.  779 
24.  709 
24.638 
24.  568 

24.  498 

24.  426 
24.354 
24.283 
24.  211 
24.  139 

24.068 

23.  995 
23.922 
23.849 
23.  776 
23.  703 

23.  630 

23.556 
23.  482 
23.408 
23.334 
23.  260 

23.  186 

23.111 
23.035 
22.960 

22.885 
22.810 

22.734 

Longi- 
tude 
inter- 
val. 

42° 

43° 

11.503 
23.006 
34.510 
46.  013 
57.  516 

69.  019 

5 
10 
15 
20 
25 
30 

Inches. 
0.002 
.008 
.019 
.033 
.052 
.075 

Inches. 
0.002 
.008 
.019 
.033 
.052 
.075 

11.505 
23.010 
34.515 
46.020 
57.525 

69.030 

44° 

45° 

11.507 
23.014 
34.522 
46.029 
57.536 

69.043 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.019 
.034 
.052 
.075 

0.002 
.008 
.019 
.034 
.053 
.076 

11.509 
23.  018 
34.528 
46.037 
57.546 

69.055 

46° 

47° 

11.511 
23.023 
34.534 
46.045 
57.557 

69.068 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.019 
.034 
.063 
.076 

0.002 
.008 
.019 
.034 
.052 
.075 

11.  513 

23.027 
34.540 
46.053 
57.567 

69.080 

48° 

49° 

5 
10 
15 
20 

25 
30 

0.002 
.008 
.019 
.033 
.052 
.075 

0.002 
.008 
.019 
.033 
.052 
.075 

11.  516 
23.031 
34.546 
46.062 
57.  577 

69.093 

46061—08 5 


66  GEOGEAPHIC   TABLES    AND    FORMULAS. 

TABLE  7. — Coordinates  for  projection  of  maps  (scale  -5^-5-5) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o        / 
49    00 

10 
20 
30 
40 
50 

50    00 

10 
20 
30 
40 
5C 

51    00 

10 
20 
30 
40 
50 

52    00 

10 
20 
30 
40 
50 

53    00 

10 
20 
30 
40 
50 

54    00 

10 
20 
30 
40 
50 

55    00 

10 
20 
30 
40 
50 

56    00 

Inches. 
69.  093 

Inches. 
3.789 

3.776 
3.764 
3.751 
3.738 
3.725 

3.713 

3.700 
3.687 
3.674 
3.661 
3.648 

3.635 

3.622 
3.609 
3.596 
3.583 
3.570 

3.556 

3.543 
3.530 
3.516 
3.503 
3.490 

3.477 

3.463 
3.450 
3.436 
3.423 
3.  409 

3.396 

3.382 
3.368 
3.355 
3.341 
3.327 

3.314 

3.300 
3.286 
3.272 
3.258 
3.245 

3.231 

Inches. 

7.578 

7.553 
7.527 
7.502 
7.476 
7.451 

7.425 

7.399 
7.374 
7.348 
7.322 
7.296 

7.270 

7.244 
7.218 
7.  191 
7.165 
7.139 

7.113 

7.086 
7.060 
7.033 
7.006 
6.980 

6.953 

6.926 
6.899 
6.872 
6.845 
6.818 

6.791 

6.764 
6.737 
6.709 
6.682 
6.655 

6.628 

6.600 
6.572 
6.545 
6.517 
6.489 

6.462 

Inches. 
11.  367 

11.  329 
11.  291 
11.  253 
11.  214 
11.176 

11.138 

11.099 
11.  060 
11.021 
10.  983 
10.944 

10.905 

10.  866 
10.827 
10.  787 
10.  748 
10.  709 

10.  669 

10.629 
10.  589 
10.550 
10.  510 
10.  470 

10.430 

10.389 
10.  349 
10.309 
10.268 
10.  228 

10.187 

10.  146 
10.  105 
10.064 
10.023 
9.982 

9.941 

9.900 
9.859 
9.817 
9.776 
9.734 

9.693 

Inches. 
15.  156 

15.  105 
15.  054 
15.003 
14.  952 
14.901 

14.850 

14.  799 
14.  747 
14.  695 
14.  644 
14.  592 

14.540 

14.  488 
14.436 
14.  383 
14.  330 

14.  278 

14.226 

14.  172 
14.119 
14.066 
14.013 
13.960 

13.906 

13.852 
13.  798 
13.  745 
13.  691 
13.  637 

13.583 

13.528 
13.  474 
13.419 
13.364 
13.  310 

13.255 

'   13.200 
13.  145 
13.  089 
13.  034 
12.  979 

12.  924 

Inches. 
18.945 

18.  882 
18.  818 
18.  754 
18.690 
18.  627 

18.563 

18.499 
18.  434 
18.  369 
18.  305 
18.  240 

18.  176 

18.  110 
18.045 
17.  979 
17.  913 
17.  848 

17.  782 

17.  716 
17.649 
17.  583 
17.  516 
17.450 

17.383 

17.  316 
17.  248 
17.  181 
17.  114 
17.046 

16.979 

16.  910 
16.  842 
16.  774 
16.706 
16.  637 

16.569 

16.500 
16.  431 
16.  362 
16.  293 
16.  224 

16.  155 

Inches. 
22.  734 

22.  658 
22.  581 
22.505 
22.429 
22.  352 

22.276 

22.  198 
22.121 
22.043 
21.965 

21.888 

21.  811 

21.  732 
21.  653 
21.  574 
21.496 
21.  417 

21.  338 

21.  259 
21.  179 
21.099 
21.019 
20.  939 

20.  860 

2(7.  779 
20.  698 
20.617 
20.  536 
20.  455 

20.374 

20.292 
20.  210 
20.  128 
20.047 
19.964 

19.883 

19.800 
19.  717 
19.  634 
19.  551 
19.  468 

19.385 

Longi- 
tude 
inter- 
val. 

49° 

50° 

11.  517 
23.  035 
34.  552 
46.  070 

57.  587 

69.  105 

5 
10 
15 
20 

25 
30 

Inches. 
0.002 
.008 
.019 
.033 
.052 
.075 

Inches. 
0.002 
.008 
.019 
.033 
.052 
.075 

11.520 
23.  039 
34.558 
46.  078 
57.  598 

69.  117 

51° 

52° 

11.521 
23.043 
34.564 
46.  086 
57.  607 

69.  128 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.019 
.033 
.051 
.074 

0.002 
.008 
.018 
.033 
.051 
.073 

11.  523 
23.  047 
34.  570 
46.094 
57.  617 

69.140 

53° 

54° 

11.525 
23.051 
34.576 
46.  102 
57.  627 

69.  152 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.018 
.032 
.050 
.073 

0.002 
.008 
.018 
.032 
.050 
.072 

11.527 
23.055 
34.  582 
46.109 
57.  636 

69.164 

55° 

56° 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.018 
.032 
.049 
.071 

0.002 
.008 
.018 
.031 
.049 
.070 

11.  529 
23.059 
34.588 
46.  117 
57.646 

69.  176 

GEOGRAPHIC   TABLES   AND   FOEMTTLAS. 


67 


TABLE  7. — Coordinate*  for  projection  of  maps  (scale  ^STS) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 
56    00 

10 
20 
30 
40 
50 

57    00 

10 
20 
30 
40 
50 

58    00 

10 
20 
30 
40 
50 

59    00 

10 
20 
30 
40 

50 

60    00 

10 
20 
30 
40 
50 

61    00 

10 
20 
30 
40 

50 

62    00 

10 
20 
30 
40 
50 

63    00 

Inches. 
69.  176 

Inches. 
3.231 

3.217 
3.203 
3.189 
3.175 
3.161 

3.147 

3.133 
3.119 
3.104 
3.090 
3.076 

3.062 

3.048 
3.034 
3.019 
3.005 
2.991 

2.976 

2.962 
2.947 
2.933 
2.918 
2.904 

2.890 

2.875 
2.860 
2.846 
2.831 
2.816 

2.802 

2.787 
2.772 
2.758 
2.743 
2.728 

2.713 

2.699 
2.684 
2.669 
2.654 
2.639 

2.624 

Inches. 
6.462 

6.434 
6.406 
6.378 
6.350 
6.322 

6.294 

6.266 
6.237 
6.209 
6.181 
6.152 

6.124 

6.096 
6.067 
6.038 
6.010 
5.981 

5.953 

5.924 
5.895 
5.866 
5.837 
5.808 

5.779 

5.750 
5.721 
5.691 
5.662 
5.633 

6.604 

5.574 
5.545 
5.115 

5.486 
5.456 

5.427 

5.397 
5.367 
5.337 
5.308 
5.278 

5.248 

Inches. 
9.693 

9.651 
9.609 
9.567 
9.525 
9.483 

9.441 

9.398 
9.356 
9.314 
9.271 
9.229 

9.186 

9.143 
9.101 
9.058 
9.015 

8.972 

8.929 

8.885 
8.842 
8.799 
8.755 
8.712 

8.669 

8.625 
8.581 
8.537 
8.493 
8.450 

8.406 

8.361 
8.317 
8.273 
8.229 
8.184 

8.140 

8.0% 
8.051 
8.006 
7.961 
7.917 

7.872 

Inches. 
12.924 

12.868 
12.  812 
12.756 
12.700 
12.644 

12.588 

12.531 
12.  475 
12.  418 
12.362 
12.305 

12.248 

12.  191 
12.134 
12.  077 
12.020 
11.962 

11.905 

11.847 
11.790 
11.  732 
11.674 
11.  616 

11.558 

11.500 
11.441 
11.383 
11.  324 
11.266 

11.208 

11.148 
11.090 
11.030 
10.972 
10.  912 

10.854 

10.794 
10.734 
10.  675 
10.  615 
10.556 

10.4% 

Inches. 
16.155 

16.085 
16.  015 
15.945 
15.  875 
15.805 

15.735 

15.664 
15.594 
15.523 
15.452 
15.381 

15.  311 

15.239 
15.168 
15.0% 
15.025 
14.953 

14.882 

14.809 
14.  737 
14.665 
14.592 
14.  520 

14.448 

14.  375 
14.302 
14.229 
14.156 
14.  083 

14.  010 

13.  936 
13.862 
13.788 
13.  715 
13.  641 

13.567 

13.  493 
13.  418 
13.344 
13.  269 
13.  195 

13.120 

Inches. 
19.385 

19.301 
19.217 
19.  134 
19.050 
18.966 

18.882 

18.  797 
18.  712 
18.627 
18.542 
18.457 

18.  373 

18.287 
18.  201 
18.  115 
18.029 
17.944 

17.858 

17.  771 
17.684 
17.597 
17.510 
17.  424 

17.  337 

17.  249 
17.162 
17.  074 
16.987 
16.  899 

16.811 

16.  723 
16.634 
16.546 
16.457 
16.369 

16.280 

16.  191 
16.  102 
16.  012 
15.923 
15.  833 

15.744 

Longi- 
tude 
inter- 
val. 

56° 

57° 

11.531 
23.063 
34.594 
46.125 
57.656 

69.188 

5 
10 
15 
20 
25 
30 

Inches. 
0.002 
.008 
.018 
.031 
.049 
.070 

Inches, 
0.002 
.008 
.017 
.031 
.048 
.069 

11.533 
23.066 
34.599 
46.132 
57.666 

69.199 

58° 

59° 

11.535 
23.070 
34.605 
46.140 
57.  675 

69.  210 

5 
10 
15 
20 
25 
30 

0.002 
.008 
.017 
.030 
.047 
.068 

0.002 
.007 
.017 
.030 
.046 
.067 

11.537 
23.074 
34.610 
46.  147 

57.684 

69.221 

60° 

61° 

11.539 
23.077 
34.616 
46.154 
57.693 

69.232 

5 
10 

15 
20 
25 
30 

0.002 
.007 
.016 
.029 
.045 
.065 

0.002 
.007 
.016 
.029 
.045 
.064 

11.540 
23.081 
34.621 
46.  162 
57.702 

69.242 

62° 

63° 

5 
10 

15 
20 
25 
30 

0.002 
.007 
.016 
.028 
.044 
.063 

0.002 
.007 
.015 
.027 
.043 
.061 

11.542 
23.084 
34.626 
46.168 
57.  710 

69.253 

68  GEOGEAPHIC    TABLES    AND   FORMULAS. 

TABLE  7. — Coordinates  for  projection  of  maps  (scale  TO£OT) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o        / 
63    00 

Iv. 

20 
30 
40 
50 

64    00 

10 
20 
30 
40 
50 

65    00 

10 
20 
30 
40 

50 

66    00 

10 
20 
30 
40 
50 

67    00 

10 
20 
30 
40 

50 

68    00 

10 
20 
30 
40 
50 

69    00 

10 
20 
30 
40 

50 

70    00 

Inches. 
69.  253  . 

Inches. 
2.624 

2.609 
2.594 
2.579 
2.564 
2.549 

2.534 

2.519 
2.504 

2.488 
2.473 
2.458 

2.443 

2.428 
2.412 
2.397 
2.382 
2.366 

2.351 

2.336 
2.320 
2.305 
2.290 
2.274 

2.259 

2.243 

2.228 
2.212 
2.197 
2.181 

2.166 

2.150 
2.134 
2.119 
2.103 

2.088 

2.072 

2.056 
2.040 
2.025 
2.009 
1.993 

1.977 

Inches. 

5.248 

5.218 
5.188 
5.158 
5.128 
5.098 

5.068 

5.037 
5.007 
4.977 
4.947 
4.916 

4.886 

4.855 
4.825 
4.794 
4.764 
4.733 

4.702 

4.672 
4.641 
4.610 
4.579 
4.548 

4.518 

4.487 
4.455 
4.424 
4.393 
4.362 

4.331 

4.300 
4.269 
4.237 
4.206 
4.175 

4.144 

4.  112' 

4.081 
4.049 
4.018 
3.986 

3.955 

Inches. 

7.872 

7.827 
7.782 
7.737 
7.692 
7.647 

7.602 

7.556 
7.511 
7.465 
7.420 
'7.  374 

7.329 

7.283 
7.237 
7.191 
7.145 
7.100 

7.054 

7.007 
6.961 
6.915 
6.869 
6.823 

6.776 

6.730 
6.683 
6.637 
6.590 
6.543 

6.497 

6.450 
6.403 
6.356 
6.309 
6.263 

6.216 

6.169 
6.121 
6.074 
6.027 
5.980 

5.932 

Inches. 
10.496 

10.  436 
10.  376 
10.  316 
10.256 
10.  196 

10.  136 

10.075 
10.  014 
9.954 
9.893 
9.832 

9.772 

9.711 
9.650 
9.588 
9.527 
9.466 

9.405 

9.343 
9.282 
9.220 
9.158 
9.097 

9.035 

8.973 
8.911 

8.849 
8.787 
8.724 

8.662 

8.600 
8.538 
8.475 
8.412 
8.350 

8.288 

8.225 
8.162 
8.099 
8.036 
7.973 

7.910 

Inches. 
13.120 

13.045 
12.  970 
12.895 
12.820 
12.  745 

12.670 

12.  594 
12.  518 
12.  442 
12.367 
12.  291 

12.  215 

12.139 
12.062 
11.  986 
11.909 
11.  833 

11.756 

11.  679 
11.  602 
11.525 
11.448 
11.  371 

11.294 

11.217 
11.  139 
11.061 
10.984 
10.906 

10.  828 

10.  750 
10.  672 
10.  594 
10.  516 
10.438 

10.360 

10.281 
10.202 
10.  124 
10.  045 
9.966 

9.888 

Inches. 
15.  744 

15.  654 
15.564 
15.473 
15.  383 
15.293 

15.  203 

15.  112 

15.022 
14.930 
14.840 
14.  749 

14.658 

14.566 
14.474 
14.383 
14.291 
14.199 

14.  107 

14.  015 
13.  922 
13.830 
13.  738 
13.645 

13.553 

13.460 
13.366 
13.273 
13.  180 
13.  087 

12.  994 

12.900 
12.  806 
12.  712 
12.  619 
12.  525 

12.  431 

12.  337 
12.  242 
12.  148 
12.054 
11.  959 

11.865 

Longi- 
tude 
inter- 
val. 

63° 

64° 

11.544 
23.  087 
34.  631 
46.175 
57.718 

69.262 

5 
10 
15 
20 
25 
30 

Inches. 
0.002 
.007 
.015 
.027 
.043 
.061 

Inches. 
0.002 
.007 
.015 
.026 
.041 
.060 

11.545 
23.091 
34.636 
46.  182 
57.  727 

69.  272 

65° 

66° 

11.547 
23.  094 
34.641 

46.  188 
57.735 

69.282 

5 
10 
15 
20 
25 
30 

0.002 
.006 
.014 
.026 
.040 
.058 

0.002 
.006 
.014 
.025 
.039 
.056 

11.548 
23.097 
34.646 
46.  194 
57.  742 

69.291 

67° 

68° 

11.550 
23.100 
34.650 
46.200 
57.750 

69.300 

5 
10 
15 
20 

25 
30 

0.001 
.006 
.014 
.024 
.038 
.054 

0.001 
.006 
.013 
.023 
.036 
.053 

11.552 
23.103 
34.654 
46.206 
57.  758 

69.309 

69° 

70° 

5 
10 
15 
20 
25 
30 

0.001 
.006 
.013 
.022 
.035 
.051 

0.001 
.005 
.012 
.022 
.034 
.049 

11.553 
23.106 
34.659 
46.212 
57.764 

69.  317 

GEOGRAPHIC    TABLES    AND   FORMULAS. 


69 


TABLE  7. — Coordinates  for  projection  of  maps  (scale  ^0-5-7) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

157  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 
70    00 

10 
20 
30 
40 

50 

71    00 

10 
20 
30 
40 
50 

72    00 

10 
20 
30 
40 
50 

73    00 

10 
20 

30 
40 
50 

74    00 

10 
20 
30 
40 
50 

75    00 

10 
20 
30 
40 

50 

76    00 

10 
20 
30 
40 
50 

77    00 

Inches. 
69.  317 

Inches. 
1.977 

1.962 
1.946 
1.930 
1.914 

1.898 

1.882 

1.866 
1.850 
1.835 
1.819 
1.803 

1.787 

1.771 
1.755 
1.739 
1.723 
1.707 

1.691 

1.674 
1.658 
1.642 
1.626 
1.610 

1.594 

1.578 
1.562 
1.545 
1.529 
1.513 

1.497 

.    1.480 
1.464 
1.448 
1.432 
1.415 

1.399 

1.383 
1.366 
1.350 
1.334 
1.317 

1.301 

Inches. 
3.955 

3.923 
3.892 
3.860 
3.828 
3.796 

3.765 

3.733 
3.701 
3.669 
3.637 
3.605 

3.574 

3.542 
3.509 
3.477 
3.445 
3.413 

3.381 

3.349 
3.317 
3.284 
3.252 
3.220 

3.188 

3.155 
3.123 
3.091 
3.058 
3.026 

2.993 

2.961 
2.928 
2.896 
2.863 
2.831 

2.798 

2.765 
2.733 
2.700 
2.667 
2.634 

2.602 

Inches. 
5.932 

5.885 
5.837 
5.790 
5.742 
5.695 

5.647 

5.600 
5.552 
5.504 
5.456 
5.408 

5.360 

5.312 
5.264 
5.216 
5.168 
5.120 

5.072 

5.024 
4.975 
4.927 
4.878 
4.830 

4.782 

4.733 
4.685 
4.636 
4.587 
4.539 

4.490 

4.441 
4.392 
.4.344 
4.295 
4.246 

4.197 

4.148 
4.099 
4.050 
4.001 
3.952 

3.903 

Inches. 
7.910 

7.846 
7.783 
7.720 
7.656 
7.593 

7.530 

7.466 
7.402 
7.338 
7.275 
7.211 

7.147 

7.083 
7.019 
6.955 
6.891 
6.826 

6.762 

6.698 
6.634 
6.569 
6.504 
6.440 

6.376 

6.311 
6.246 
6.181 
6.116 
6.052 

5.987 

5.922 
5.856 
5.792 
5.726 
•      5.  661 

5.5% 

5.530 
5.465 
5.400 
5.334 
5.269 

5.204 

Inches. 

9.888 

9.808 
9.729 
9.650 
9.571 
9.491 

9,412 

9.333 
9.253 
9.173 
9.094 
9.014 

8.934 

8.854 
8.774 
8.694 
8.614 
8.533 

8.453 

8.373 
8.292 
8.211 
8.131 
8.050 

7.970 

7.889 
7.808 
7.727 
7.645 
7.565 

7.484 

7.402 
7.321 
7.240 
7.158 
7.077 

6.995 

6.913 
6.832 
6.750 
6.668 
6.586 

6.505 

Inches. 
11.865 

11.  770 
11.  675 
11.  579 
11.485 
11.  389 

11.294 

11.  199 
11.  103 
11.008 
10.  912 
10.  816 

10.  721 

10.  625 
10.528 
10.  432 
10.336 
10.  240 

10.  144 

10.047 
9.950 
9.853 
9.757 
9.660 

9.563 

9.466 
9.369 
9.272 
9.175 
9.077 

8.980 

8.882 
8.785 
8.687 
8.590 
8.492 

8.394 

8.296 
8.198 
8.099 
8.002 
7.903 

7.805 

Longi 
tude 
inter- 
val. 

70° 

71° 

11.554 
23.109 
34.663 
46.217 
57.  772 

69.326* 

/ 
5 
10 
15 
20 
25 
30 

Inches. 
0.001 
.005 
.012 
.022 
.034 
.049 

Inches. 
0.001 
.005 
.012 
.021 
.032 
.047 

11.556 
23.111 
34.667 
46.222 
57.  778 

69.334 

72° 

73° 

11.557 
23.114 
34.670 
46.227 
57.784 

69.341 

5 
10 
15 
20 
25 
30 

0.001 
.005 
.011 
.020 
.031 
.044 

0.001 
.005 
.011 
.019 
.029 
.042 

11.558 
23.116 
34.674 
46.232 
57.790 

69.348 

74° 

75° 

11.559 
23.118 
34.677 
46.236 
57.796 

69.355 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.010 
.018 
.028 
.040 

0.001 
.004 
.009 
.017 
.026 
.038 

11.560 
23.120 
34.681 
46.241 
57.801 

69.361 

76° 

77° 

5 
10 
15 
20 
25 
30 

0.001 
.004 
.009 
.016 
.025 
.036 

0.001 
.004 
.008 
.015 
.023 
.033 

11.561 
23.122 
34.683 
46.244 
57.806 

69.  367 

70 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  7. — Coordinates  for  projection  of  maps  (scale  -$-3^-5-0) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

5'  longi- 
tude. 

10'  longi- 
tude. 

15'  longi- 
tude. 

20'  longi- 
tude. 

25'  longi- 
tude. 

30'  longi- 
tude. 

o       / 

77    00 

10 

20 
30 
40 
50 

78    00 

10 
20 
30 
40 
50 

79    00 

10 
20 
30 
40 
50 

80    00 

Inches. 
69.  367 

Inches. 
1.301 

1.284 
1.268 
1.252 
1.235 
1.219 

1.202 

1.186 
1.169 
1.153 
1.136 
1.120 

1/104 

1.087 
1.070 
1.054 
1.037 
1.021 

1.004 

Inches. 
2.602 

2.569 
2.536 
2.503 
2.470 
2.438 

2.405 

2.372 
2.339 
2.306 
2.273 
2.240 

2.207 

2.174 
2.  141 
2.108 
2.075 
2.042 

2.009 

Inches. 
3.903 

3.854 
3.804 
3.765 
3.706 
3.656 

3.607 

3.558 
3.508 
3.459 
3.410 
3.360 

3.311 

3.261 
3.211 
3.162 
3.112 
3.062 

3.013 

Inches. 
5.204 

5.138 
5.072 
5.006 
4.941 

4.875 

4.810 

4.744 

4.678 
4.612 
4.546 
4.480 

4.414 

4.348 
4.282 
4.216 
4.150 
4.083 

4.017 

Inches. 
6.505 

6.423 
6.341 
6.258 
6.176 
6.094 

6.012 

5.930 
5.847 
6.765 
5.683 
5.600 

5.518 

5.435 
5.352 
5.270 
5.187 
5.104 

5.022 

Inches. 
7.805 

7.707 
7.609 
7.510 
7.411 
7.313 

7.214 

7.115 
7.016 
6.918 
6.819 
6.720 

6.621 

6.522 
6.422 
6.323 
6.  224 
6.125 

6.026 

Longi- 
tude 
inter- 
val. 

77° 

78° 

11.562 
23.  124 
34.686 
46.  248 
57.  810 

69.  373 

5 
10 
15" 
20 
25 
30 

Inches. 
0.001 
.004 
.008 
.015 
.023 
.033 

Inches. 
0.001 
.003 
.008 
.014 
.021 
.031 

11.563 
23.  126 
34.689 
46.252 
57.814 

69.  377 

79° 

80° 

11.564 
23.127 
34.691 
46.255 

57.  818 

69.382 

5 
10 
15 
20 
25 
30 

0.001 
.003 
.007 
.013 
.020 
.028 

0.001 
.003 
.006 
.011 
.018 
.026 

GEOGRAPHIC    TABLES    AND   FORMULAS. 

TABLE  8. — Coordinates  for  projection  of  maps  (scale 


71 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

2i'  longi- 
tude. 

5'  longi- 
tude. 

7i'  longi- 
tude. 

10'  longi- 
tude. 

12|'  lon- 
gitude. 

15'  longi- 
tude. 

o       / 
25    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

26    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

27    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
60 
55 

28    00 
05 
10 
15 
20 
26 
30 
35 
40 
45 
50 
56 

29    00 

Inches. 

Inches. 
2.650 
2.648 
2.646 
2.644 
2.642 
2.641 
2.639 
2.637 
2.635 
2.633 
2.  631 
2.630 

2.628 
2.626 
2.624 
2.622 
2.620 
2.618 
2.617 
2.615 
2.613 
2.611 
2.609 
2.607 

2.605 
2.603 
2.601 
2.599 
2.  597 
2.595 
2.593 
2.591 
2.590 
2.588 
2.586 
2.584 

2.582 
2.580 
2.578 
2.576 
2.574 
2.572 
2.570 
2.568 
2.566 
2.564 
2.562 
2.560 

2.558 

Inches. 
5.299 
5.296 
5.292 
5.288 
5.285 
5.281 
5.277 
5.274 
5.270 
5.266 
5.263 
5.259 

5.256 
5.252 
5.  248 
5.244 
5.241 
5.237 
5.233 
5.229 
5.225 
5.222 
5.218 
5.214 

5.210 
6.207 
5.203 
5.199 
5.195 
5.191 
5.187 
5.183 
5.179 
5.175 
5.171 
5.167 

5.163 
5.159 
5.155 
5.151 
5.147 
5.143 
6.139 
5.135 
5.131 
5.127 
5.123 
5.119 

5.115 

Inches. 
7.949 
7.944 
7.938 
7.933 
7.927 
7.922 
7.916 
7.911 
7.905 
7.900 
7.894 
7.889 

7.883 
7.878 
7.872 
7.866 
7.861 
7.855 
7.849 
7.844 
7.838 
7.833 
7.827 
7.821 

7.816 
7.810 
7.804 
7.798 
7.792 
7.786 
7.780 
7.774 
7.769 
7.763 
7.757 
7.751 

7.745 
7.739 
7.733 

7.727 
7.721 
7.715 
7.709 
7.703 
7.697 
7.691 
7.685 
7.679 

7.673 

Inches. 
10.  599 
10.  591 
10.584 
10.  577 
10.569 
10.562 
10.555 
10.548 
10.540 
.  10.  533 
10.  526 
10.  518 

10.  511 
10.504 
10.496 
10.  489 
10.481 
10.  473 
10.466 
10.458 
10.451 
10.  443 
10.  436 
10.  428 

10.  421 
10.  413 
10.  405 
10.397 
10.389 
10.382 
10.  374 
10.  366 
10.358 
10.350 
10.  342 
10.335 

10.  327 
10.  319 
10.  311 
10.303 
10.294 
10.286 
10.  278 
10.  270 
10.262 
10.254 
10.  246 
10.238 

10.230 

Inches. 
13.  248 
13.  239 
13.  230 
13.221 
13.  212 
13.203 
13.  194 
13.  184 
13.  175 
13.  166 
13.  157 
13.  148 

13.  139 
13.  129 
13.  120 
13.  Ill 
13.  101 
13.092 
13.  082 
13.  073 
13.064 
13.054 
13.045 
13.035 

13.026 
13.  016 
13.006 
12.997 
12.  987 
12.  977 
12.967 
12.  957 
12.  948 
12.938 
12.928 
12.918 

12.908 
12.  898 
12.888 
12.  878 
12.  868 
12.858 
12.848 
12.838 
12.828 
12.  818 
12.808 
12.  798 

12.788 

Inches. 
15.898 
15.887 
15.  876 
15.865 
15.854 
15.843 
15.832 
15.  821 
15.810 
15.799 
15.  788 
15.  777 

15.  766 
15.  755 
15.  744 
15.  733 
15.  721 
15.  710 
15.699 
15.688 
15.  676 
15.665 
15.654 
15.642 

15.  631 
15.  620 
15.608 
15.596 
15.584 
15.  572 
15.  561 
15.549 
15.537 
15.  525 
15.  514 
15.502 

15.490 
15.  478 
15.466 
15.454 
15.  442 
15.430 
15.  418 
15.  405 
15.  393 
15.  381 
15.369 
15.  357 

15.345 

Longi- 
tude 
inter- 
val. 

25° 

26° 

5.815 
11.629 
17.  444 
23.259 
29.074 
34.888 

/ 

2i 
5 
7* 
10 
12i 
15 

Inches. 
0.000 
.002 
.004 
.007 
.010 
.015 

Inches. 
0.000 
.002 
.004 
.007 
.010 
.015 

5.816 
11.631 
17.447 
23.262 
29.  078 
34.893 

27° 

2i 

5 

i? 

m 

15 

Inches. 
0.000 
.002 
.004 
.007 
.011 
.015 

«6.816 
11.633 
17.449 
23.265 
29.082 
34.898 

27° 

28° 

2£ 
5 
7£ 
10 
12^ 
15 

Inches. 
0.000 
.002 
.004 
.007 
.011 
.015 

Inches. 
0.000 
.002 
.004 
.007 
.011 
.016 

5.817 
11.634 
17.451 
23.268 
29.085 
34.903 

29° 

'? 
$ 
JP 

Inches. 
0.000 
.002 
.004 
.007 
.011 
.016 

72  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  8. — Coordinates  for  projection  of  maps  (scale  ralrnr) — Continued. 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

21'longi 
tude. 

5'  longi- 
tude. 

74'  longi- 
tude. 

10'longi 
tude. 

121'  lon- 
gitude. 

15'longi 
tude. 

o      t 
29    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

30    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

31    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

32    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

33    00 

Inches, 

Inches. 
2.558 
2.555 
2.553 
2.551 
2.549 
2.547 
2.545 
2.543 
2.541 
2.539 
2.537 
2.535 

2.533 
2.530 
2.528 
2.526 
2.524 
2.522 
2.520 
2.  518 
2.515 
2.  513 
2.511 
2.509 

2.507 
2.505 
2.502 
2.500 
2.498 
2.496 
2.494 
2.491 
2.489 
2.487 
2.485 
2.482 

2.  480 
2.478 
2.476 
2.473 
2.471 
2.469 
2.467 
2.464 
2.462 
2.460 
2.458 
2.455 

2.453 

Inches. 
5.115 
5.111 
5.107 
5.103 
5.098 
5.094 
5.090 
5.086 
5.082 
5.078 
5.073 
5.069 

5.065 
5.061 
5.057 
5.052 
5.048 
5.044 
5.039 
5.035 
5.031 
5.026 
5.022 
5.018 

5.014 
5.009 
5.005 
5.000 
4.996 
4.991 
4.987 
4.983 
4.978 
4.974 
4.969 
4.965 

4.960 
4.956 
4.951 
4.947 
4.942 
4.938 
4.933 
4.929 
4.924 
4.920 
4.915 
4.910 

4.906 

Inches. 
7.673 
7.666 
7.660 
7.654 
7.648 
7.641 
7.635 
7.629 
7.623 
7.616 
7.610 
7.604 

7.598 
7.591 
7.585 
7.578 
7.572 
7.565 
7.559 
7.552 
7.546 
7.540 
7.533 
7.527 

7.520 
7.514 
7.507 
7.500 
7.494 
7.487 
7.480 
7.474 
7.467 
7.460 
7.454 
7.447 

7.441 
7.434 
7.427 
7.420 
7.413 
7.  407 
7.400 
7.  393 
7.386 
7.379 
7.372 
7.366 

7.359 

Inches. 
10.  230 
10.  222 
10.  213 
10.  205 
10.  197 
10.  188 
10.  180 
10.  172 
10.164 
10.155 
10.  147 
10.  138 

10.130 
10.122 
10.  113 
10.104 
10.0% 
10.087 
10.  079 
10.  070 
10.061 
10.  053 
10.044 
10.036 

10.027 
10.  018 
10.009 
10.000 
9.992 
9.983 
9.974 
9.965 
9.956 
9.947 
9.938 
9.930 

9.921 
9.912 
9.903 
9.894 
9.884 
9.875 
9.866 
9.857 
9.848 
9.839 
9.831 
9.821 

9.  812 

Inches. 
12.788 
12.  777 
12.  767 
12.  756 
12.  746 
12.  735 
12.  725 
12.  715 
12.  704 
12.694 
12.  684 
12.  673 

12.663 
12.  652 
12.641 
12.630 
12.  620 
12.609 
12.  598 
12.587 
12.  577 
12.566 
12.  -555 
12.544 

12.534 
12.  523 
12.  512 
12.500 
12.489 
12.  478 
12.  467 
12.456 
12.445 
12.  434 
12.423 
12.  412 

12.  401 
12.  390 
12.378 
12.  367 
12.356 
12.344 
12.333 
12.  322 
12.  310 
12.  299 
12.287 
12.  276 

12.  265 

Inches. 
15.  345 
15.  333 
15.  320 
15.  308 
15.295 
15.  283 
15.270 
15.  258 
15.  245 
15.  233 
15.220 
15.  208 

15.  195 
15.  182 
15.  169 
15.  157 
15.144 
15.  131 
15.  118 
15.  105 
15.  092 
15.  079 
15.066 
15.053 

15.040 
15.027 
15.  014 
15.000 
14.  987 
14.  974 
14.961 
14.948 
14.  934 
14.921 
14.908 
14.  894 

14.881 
14.  868 
14.854 
14.840 
14.  827 
14.  813 
14.800 
14.  786 
14.  772 
14.  759 
14.  745 
14.  731 

14.  718 

Longi- 
tude 
inter- 
val. 

29° 

30° 

5.818 
11.  636 
17.454 
23.272 
29.090 
34.908 

2| 
5 
71 
10 

124 

15 

Inches. 
0.000 
.002 
.004 
.007 
.011 
.016 

Inches. 
0.000 
.002 
.004 
.007 
.012 
.017 

5.819 
11.638 
17.457 
23.276 
29.  095 
34.913 

31° 

24 

5 

71 
10 

11* 

0.000 
.002 
.004 
.008 
.012 
.017 

5.820 
11.640 
17.460 
23.280 
29.100 
34.919 

Longi- 
tude 
inter- 
val. 

31° 

32° 

21 
5 
71 
10 
121 
15 

Inches. 
0.000 
.002 
.004 
.008 
.012 
.017 

Inches. 
0.000 
.002 
.004 
.008 
.012 
.017 

5.821 
11.642 
17.  462 
23.283 
29.104 
34.925 

33° 

21 
5 
71 
10 
121 
15 

0.000 
.002 
.004 
.008 
.012 
.017 

GEOGRAPHIC    TABLES    AND   FORMULAS. 


73 


TABLE  8. — Coordinates  for  projection  of  maps  (scale  srl^) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

2i'  longi- 
tude. 

5'  longi- 
tude. 

7i'  longi- 
tude. 

10'  longi- 
tude. 

12£'  lon- 
gitude. 

15'  longi- 
tude. 

o      / 
33    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

34    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

35    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

36    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

37    00 

Inches. 

Inches. 
2.453 
2.451 
2.448 
2.446 
2.444 
2.441 
2.439 
2.437 
2.434 
2.432 
2.430 
2.427 

2.425 
2.423 
2.420 
2.418 
2.415 
2.413 
2.411 
2.408 
2.406 
2.403 

Inches. 
4.906 
4.901 

4.897 
4.892 
4.887 
4.882 
4.878 
4.873 
4.868 
4.864 
4.859 
4.854 

4.850 
4.845 
4.840 
4.835 
4.831 
4.826 
4.821 
4.816 
4.811 
4.807 
4.802 
4.797 

4.792 

4.787 
4.782 
4.777 
4.773 
4.768 
4.763 
4.758 
4.753 
4.748 
4.743 
4.738 

4.733 
4.728 
4.723 
4.718 
4.713 
4.708 
4.703 
4.698 
4.693 
4.688 
4.683 
4.678 

4.673 

Inches. 
7.359 
7.352 
7.345 
7.338 
7.331 
7.324 
7.317 
7.310 
7.303 
7.2% 
7.289 
7.2S2 

7.275 
7.267 
7.260 
7.253 
7.246 
7.239 
7.231 
7.224 
7.217 
7.210 
7.203 
7.195 

7.188 
7.181 
7.174 
7.166 
7.159 
7.151 
7.144 
7.137 
7.129 
7.122 
7.115 
7.107 

7.100 
7.092 
*    7.085 
7.077 
7.070 
7.062 
7.055 
7.047 
7.039 
7.032 
7.024 
7.017 

7.009 

Inches. 
9.312 
9.802 
9.793 
9.784 
9.774 
9.765 
9.756 
9.746 
9.737 
9.728 
9.718 
9.709 

9.700 
9.690 
9.680 
9.671 
9.661 
9.652 
9.642 
£.632 
9.623 
9.613 
9.604 
9.594 

9.584 
9.574 
9.565 
9.555 
9.545 
9.535 
9.525 
9.516 
9.506 
9.496 
9.486 
9.476 

9.466 
9.456 
9.446 
9.436 
9.426 
9.416 
9.406 
9.396 
9.386 
9.376 
9.366 
9.356 

9.345 

Inches. 
12.  265 
12.253 
12.  241 
12.  230 
12.  218 
12.206 
12.  195 
12.183 
12.  171 
12.  160 
12.148 
12.  136 

12.  124 
12.  112 
12.100 
12.088 
12.076 
12.064 
12.  052 
12.  040 
12.028 
12.  016 
12.004 
11.992 

11.980 
11.968 
11.  956 
11.944 
11.  931 
11.  919 
11.907 
11.  895 
11.882 
11.  870 
11.858 
11.845 

11.833 
11.  820 
11.  808 
11.  795 
11.  783 
11.  770 
11.758 
11.  745 
11.  732 
11.  720 
11.  707 
11.694 

11.682 

Inches. 
14.  718 
14.704 
14.690 
14.  676 
14.  662 
14.648 
14.  633 
14.  619 
14.  605 
14.  591 
14.  577 
14.563 

14.549 
14.535 
14.  520 
14.506 
14.492 
14.  477 
14.  463 
14.448 
14.  434 
14.420 
14.  405 
14.  391 

14.  376 
14.  362 
14.  347 
14.332 
14.  318 
14.  303 
14.288 
14.  273 
14.259 
14.244 
14.229 
14.  214 

14.200 
14.  185 
14.  169 
14.  154 
14.  139 
14.  124 
14.109 
14.094 
14.  079 
14.064 
14.048 
14.  033 

14.018 

Longi- 
tude 
inter- 
val. 

33° 

34° 

5.822 
11.643 
17.465 
23.287 
29.109 
34.930 

V 

7£ 
10 
12* 
15 

Inches. 
0.000 
.002 
.004 
.008 
.012 
.017 

Inches. 
0.000 
.002 
.004 
.008 
.012 
.018 

35° 

5.823 
11.645 
17.468 
23.291 
29.113 
34.936 

> 

7£ 
10 

m 

15 

Inches. 
0.000 
.002 
.004 
.008 
.012 
.018 

2.401 
2.399 

2.3% 
2.394 
2.391 
2.389 
2.386 
2.384 
2.381 
2.379 
2.376 
2.374 
2.372 
2.369 

2.367 
2.364 
2.362 
2.359 
2.357 
2.354 
2.352 
2.349 
2.346 
2.344 
2.341 
2.339 

2.336 

5.824 
11.  647 
17.  471 
23.294 
29.118 
34.942 

Longi- 
tude 
inter- 
val. 

35° 

36° 

'? 
3? 

}?• 

Inches. 
0.000 
.002 
.004 
.008 
.012 
.018 

Inches 
0.001 
.002 
.005 
.008 
.013 
.018 

5.824 
11.649 
17.473 
23.297 
29.122 
34.946 

37° 

i 

2i 
5 
7* 
10 
12* 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.018 

74 


GEOGRAPHIC   TABLES    AND   FORMULAS. 


TABLE  8. — Coordinates  for  projection  of  maps  (scale  ^^0) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

2£'  longi- 
tude. 

5'  longi- 
tude. 

7i'  longi- 
tude. 

10'  longi- 
tude. 

12i'  lon- 
gitude. 

15'  longi- 
tude. 

0          / 

37    00 
05 
10 
16 
20 
25 
30 
35 
40 
45 
50 
55 

38    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

39    00 
05 
10 
15 
20 
26 
30 
35 
40 
45 
50 
55 

40    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

41    00 

Inches. 

Inches. 
2.336 
2.  334 
2.331 
2.329 
2.326 
2.323 
2.321 
2.318 
2.316 
2.313 
2.311 
2.308 

2.305 
2.303 
2.300 
2.298 
2.295 
2.292 
2.290 
2.287 
2.284 
2.382 
2.279 
2.276 

2.274 
2.271 
2.268 
2.266 
2.263 
2.260 
2.258 
2.255 
2.  252 
2.250 
2.247 
2.244 

2.241 
2.239 
2.236 
2.233 
2.230 
2.228 
2.225 
2.222 
2.219 
2.217 
2.214 
2.211 

2.208 

Inches. 
4.673 
4.667 
4.662 
4.657 
4.652 
4.647 
4.642 
4.637 
4.631 
4.626 
4.621 
4.616 

4.611 
4.606 
4.600 
4.595 
4.590 
4.584 
4.579 
4.574 
4.569 
4.563 
4.558 
4.553 

4.547 
4.542 
4.537 
4.531 
4.  526 
4.521 
4.515 
4.510 
4.504 
4.499 
4.494 
4.488 

4.483 
4.477 
4.472 
4.466 
4.461 
4.455 
4.450 
4.444 
4.439 
4.433 
4.428 
4.422 

4.417 

Inches. 
7.009 
7.001 
6.994 
6.986 
6.978 
6.970 
6.963 
6.955 
6.947 
6.939 
6.932 
6.924 

6.916 

6.908 
6.900 
6.892 
6.885 
6.877 
6.869 
6.861 
6.853 
6.845 
6.837 
6.829 

6.821 
6.813 
6.805 
6.797 
6.789 
6.781 
6.773 
6.765 
6.757 
6.748 
6.740 
6.732 

6.724 
6.716 
6.708 
6.699 
6.691 
6.683 
6.675 
6.666 
6.658 
6.650 
6.642 
6.633 

6.625 

Inches. 
9.345 
9.335 
9.  325 
9.314 
9.304 
9.294 
9.283 
9.273 
9.263 
9.253 
9.  242 
9.232 

9.222 
9.211 
9.201 
9.190 
9.179 
9.169 
9.158 
9.148 
^.137 
9.127 
9.116 
9.106 

9.095 
9.084 
9.073 
9.063 
9.052 
9.041 
9.030 
9.020 
9.009 
8.998 
8.987 
8.976 

8.966 
8.955 
8.944 
8.933 
8.922 
8.911 
8.899 
8.888 
8.877 
8.866 
8.855 
8.844 

8.  833 

Inches. 
11.  682 
11.  669 
11.656 
11.  643 
11.  630 
11.  617 
11.  604 
11.  591 
11.  578 
11.566 
11.  553 
11.540 

11.  527 
11.  514 
11.501 
11.488 
11.  474 
11.461 
11.448 
11.435 
11.  422 
11.408 
11.  395 
11.  382 

11.  369 
11.  355 
11.  342 
11.  328 
11.  315 
11.301 
11.288 
11.274 
11.261 
11.  247 
11.234 
11.  221 

11.207 
11.  193 
11.180 
11.  166 
11.  152 
11.  138 
11.  124 
11.  Ill 
11.097 
11.083 
11.069 
11.056 

11.042 

Inches. 
14.  018 
14.003 
13.  987 
13.  972 
13.  956 
13.  941 
13.  925 
13.  910 
13.  894 
13.  879 
13.  863 
13.  848 

13.  832 
13.  817 
13.801 
13.  785 
13.  769 
13.  753 
13.  737 
13.  722 
13.  706 
13.690 
13.  674 
13.658 

13.  642 
13.  626 
13.  610 
13.  594 
13.  578 
13.  562 
13.  545 
13.  529 
13.  513 
13.  497 
13.481 
13.465 

13.448 
13.  432 
13.  415 
13.  399 
13.382 
13.  366 
13.349 
13.  333 
13.  316 
13.300 
13.283 
13.  267 

13.250 

Longi- 
tude 
inter- 
val. 

37° 

38° 

5.826 
11.651 
17.  477 
23.302 
29.  128 
34.954 

f 

7£ 
10 
12^ 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.018 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

""5."  827" 
11.  653 
17.480 
23.306 
29.133 
34.960 

39° 

21 
5 
7i 
10 

12* 

15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

5.828 
11.655 
17.  483 
23.310 
29.138 
34.966 

Longi- 
tude 
inter- 
val. 

39° 

40° 

f 

U 
10 

12i 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

Indies. 
0.001 
.002 
.005 
.008 
.013 
.019 

5.829 
11.  657 
17.486 
23.  314 
29.  143 
34.972 

41° 

2£ 
5 
7i 
10 

12* 

15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

GEOGRAPHIC   TABLES   AND   FORMULAS. 


75 


TABLE  S. — Coordinates  for  projection  of  maps  (scale  ssi^y) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

Zi'longi- 
tude. 

5'  longi- 
tude. 

IV  longi- 
tude. 

10'  longi- 
tude. 

12A'  lon- 
gitude. 

15'  longi- 
tude. 

O            1 

41    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

42    00 
05 
10 
15 
20 
26 
30 
35 
40 
45 
50 
55 

43    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

44    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

45    00 

Inches. 

Inches. 
2.208 
2.206 
2.203 
2.200 
2.197 
2.194 
2.192 
2.189 
2.186 
2.183 
2.180 
2.178 

2.175 
2.172 
2.169 
2.166 
2.163 
2.160 
2.158 
2.155 
2.152 
2.149 
2.146 
2.  143. 

2.140 
2.137 
2.134 
2.132 
2.129 
2.126 
2.123 
2.120 
2.117 
2.114 
2.111 
2.108 

2.105 
2.102 
2.099 
2.096 
2.093 
2.090 
2.087 
2.084 
2.081 
2.078 
2.076 
2.073 

2.070 

Inches. 
4.417 
4.411 
4.406 
4.400 
4.394 
4.389 
4.383 
4.377 
4.372 
4.366 
4.361 
4.355 

4.349 
4.344 
4.338 
4.332 
4.326 
4.321 
4.315 
4.309 
4.304 
4.298 
4.292 
4.286 

4.281 
4.275 
4.269 
4.263 
4.257 
4.251 
4.246 
4.240 
4.234 
4.228 
4.222 
4.216 

4.210 
4.205 
4.199 
4.193 
4.187 
4.181 
4.175 
4.169 
4.163 
4.157 
4.151 
4.145 

4.139 

Inqhes. 
6.  625 
6.617 
6.608 
6.600 
6.591 
6.583 
6.575 
6.566 
6.558 
6.549 
6.541 
6.533 

6.524 
6.515 
6.507 
6.498 
6.490 
6.481 
6.  472 
6.464 
6.455 
6.447 
6.438 
6.429 

6.421 
6.412 
6.403 
6.395 
6.386 
6.377 
6.368 
6.359 
6.351 
6.342 
6.333 
6.324 

6.316 
6.307 
6.298 
6.289 
6.280 
6.271 
6,262 
6.253 
6.244 
6.235 
6.227 
6.218 

6.209 

Inches. 
8.833 
8.822 
8.811 
8.800 
8.789 
8.777 
8.766 
8.755 
8.744 
8.732 
8.721 
8.710 

8.699 
8.687 
8.676 
8.664 
8.653 
8.641 
8.630 
8.618 
8.607 
8.596 
8.584 
8.573 

8.561 
8.550 
8.538 
8.526 
8.514 
8.503 
8.491 
8.479 
8.468 
8.456 
8.444 
8.432 

8.421 
8.409 
8.397 
8.385 
8.373 
8.361 
8.350 
8.338 
8.326 
8.314 
8.302 
8.290 

8.278 

Inches. 
11.042 
11.028 
11.014 
11.000 
10.  986 
10.  972 
10.  958 
10.944 
10.930 
10.  916 
10.902 
10.888 

10.  873 
10.859 
10.845 
10.830 
10.  816 
10.802 
10.  787 
10.  773 
10.  759 
10.744 
10.  730 
10.  716 

10.  701 
10.687 
10.672 
10.658 
10.643 
10.628 
10.  614 
10.599 
10.585 
10.  670 
10.555 
10.541 

10.  526 
10.  511 
10.496 
10.  482 
10.  467 
10.  452 
10.  437 
10.  422 
10.407 
10.392 
10.  377 
10.363 

10.348 

Inches. 
13.250 
13.  233 
13.216 
13.200 
13.183 
13.166 
13.  149 
13.  132 
13.  115 
13.  099 
13.082 
13.  065 

13.048 
13.  031 
13.  014 
12.996 
12.  979 
12.  962 
12.945 
12.928 
12.  910 
12.893 
12.  876 
12.859 

12.842 
12.  824 
12.807 
12.  789 
12.  772 
12.754 
12.  736 
12.  719 
12.  701 
12.684 
12.666 
12.649 

12.631 
12.613 
12.596 
12.578 
12.560 
12.542 
12.524 
12.506 
12.489 
12.471 
12.453 
12.435 

12.417 

Longi- 
tude 
inter- 
val. 

41° 

42° 

5.830 
11.659 
17.489 
23.319 
29.149 
34.978 

'9. 
,54 
J? 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

5.831 
11.661 
17.492 
23.323 
29.154 
34.984 

43° 

'l4 

7* 
10 
12* 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

Longi- 
tude 
inter- 
val. 

43° 

44° 

5.832 
11.663 
17.495 
23.327 
29.159 
34.990 

2* 
5 

$ 

m 

15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

Inches. 
0.001 
.002 
.005 
.009 
.013 
.019 

5.833 
11.666 
17.498 
23.331 
29.164 
34.997 

45° 

2i 
5 
7i 
10 
124 
15 

Inches. 
0.001 
.002 
.005 
.009 
.013 
.019 

76 


GEOGRAPHIC   TABLES   AND    FORMULAS. 


TABLE  8. — Coordinates  for  projection  of  maps  (scale  TI^) — Continued. 
[From  Smithsonian  Geographical  Tables.] 


Lati- 
tude of 
parallel. 

Meridio- 
nal dis- 
tances 
from 
even 
degree 
parallels. 

Abscissas  of  developed  parallel. 

Ordinates  of  developed 
parallel. 

2i'longi 
tude. 

5'  longi- 
tude. 

7£'  longi- 
tude. 

10'longi 
tude. 

12F  lon- 
gitude. 

15'longi 
tude. 

0           / 

45    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

46    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

47    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
'     50 
55 

48    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

49    00 
05 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

50    00 

Inches. 

Inches. 
2.070 
2.067 
2.064 
2.061 
2.058 
2.054 
2.051 
2.048 
2.045 
2.042 
2.039 
2.036 

2.033 
2.030 
2.027 
2.024 
2.021 
2.018 
2.015 
2.012 
2.009 
2.006 
2.003 
1.999 

1.996 
1.993 
1.990 
1.987 
1.984 
1.981 
1.977 
1.974 
1.971 
1.968 
1.965 
1.962 

1.959 
1.956 
1.952 
1.949 
1.946 
1.943 
1.940 
1.937 
1.933 
1.930 
1.927 
1.924 

1.921 
1.917 
1.914 
1.911 
1.908 
1.905 
1.901 
1.898 
1.895 
1.892 
1.888 
1.885 

1.882 

Inches. 
4.139 
4.133 
4.127 
4.121 
4.115 
4.109 
4.103 
4.097 
4.091 
4.085 
4.079 
4.073 

4.067 
4.060 
4.054 
4.048 
4.042 
.036 
.030 
4.023 
.017 
.011 
4.005 
3.999 

3.993 
3.986 
3.980 
3.974 
3.968 
3.961 
3.955 
3.949 
3.943 
3.936 
3.  930 
3.924 

3.917 
3.911 
3.905 
3.898 
3.892 
3.886 
3.879 
3.873 
3.867 
3.860 
3.854 
3.848 

3.841 
3.835 
3.828 
3.822 
3.815 
3.809 
3.802 
3.796 
3.790 
3.783 
3.777 
3.770 

3.764' 

Inches. 
6.209 
6.200 
6.191 
6.181 
6.172 
6.163 
6.154 
6.145 
6.136 
6.127 
6.118 
6.109 

6.100 
6.091 
6.081 
6.072 
6.063 
6.054 
6.044 
6.035 
6.026 
6.017 
6.008 
5.998 

5.989 
5.980 
5.970 
5.961 
5.951 
5.  942 
5.933 
5.923 
5.914 
5.904 
5.895 
5.886 

5.876 
5.867 
5.857 
5.848 
5.838 
5.829 
5.819 
5.810 
5.800 
5.790 
5.781 
5.771 

5.762 
5.752 
5.742 
5.733 
5.723 
5.713 
5.704 
5.694 
5.684 
5.675 
5.665 
5.655 

5.646 

Inches. 
8.278 
8.266 
8.254 
8.242 
8.230 
8.218 
8.206 
8.194 
8.181 
8.169 
8.157 
8.145 

8.133 
8.121 
8.108 
8.096 
8.084 
8.072 
8.059 
8.047 
8.035 
8.022 
8.010 
7.998 

7.985 
7.973 
7.960 
7.948 
7.935 
7.923 
7.910 
7.898' 
7.885 
7.872 
7.860 
7.848 

7.835 
7.822 
7.810 
7.797 
7.784 
7.771 
7.759 
7.746 
7.733 
7.721 
7.708 
7.695 

7.682 
7.670 
7.657 
7.644 
7.631 
7.618 
7.605 
7.592 
7.579 
7/566 
7.553 
7.540 

7.528 

Inches. 
10.  348 
10.  333 
10.  318 
10.  302 
10.  287 
10.  272 
10.  257 
10.  242 
10.  227 
10.  212 
10.  197 
10.  182 

10.  166 
10.  151 
10.  136 
10.  120 
10.  105 
10.  090 
10.  074 
10.  059 
10.  043 
10.  028 
10.013 
9.997 

9.982 
9.966 
9.950 
9.935 
9.919 
9.903 
9.888 
9.872 
9.856 
9.841 
9.825 
9.809 

9.794 
9.778 
9.763 
9.746 
9.730 
9.714 
9.698 
9.683 
9.667 
9.651 
9.635 
9.619 

9.603 
9.587 
9.571 
9.555 
9.538 
9.522 
9.506 
9.490 
9.474 
9.458 
9.442 
9.426 

9.409 

Inches. 
12.  417 
12.  399 
12.  381 
12.  363 
12.  345 
12.  327 
12.  308 
12.290 
12.  272 
12.  254 
12.  236 
12.  218 

12.  200 
12.  181 
12.  163 
12.  144 
12.  126 
12.  107 
12.  089 
12.  070 
12.052 
12.  033 
12.015 
11.996 

11.978 
11.  959 
11.940 
11.922 
11.903 
11.884 
11.865 
11.846 
11.  828 
11.  809 
11.790 
11.  771 

11.  752 
11.733 
1J.714 
11.695 
11.676 
11.657 
11.  638 
11  619 
11.600 
11.581 
11.562 
11.543 

11.524 
11.504 
11.  485 
11.466 
11.446 
11.427 
11.407 
11.388 
11.  369 
11.349 
11.330 
31.311 

11.291 

Longi- 
tude 
inter- 
val. 

45° 

46° 

5.834 
11.  668 
17.  501 
23.335 
29.  169 
35.003 

24 

5 

,5* 
* 

Inches. 
0.001 
.002 
.005 
.009 
.013 
.019 

Inches. 
0.001 
.002 
.005 
.009 
.013 
.019 

5.835 
11.  670 
17.504 
23.  339 
29.  174 
35.009 

47° 

'  f 
i? 

12J 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

5.836 
11.  672 
17.508 
23.344 
29.180 
35.015 

Longi- 
tude 
inter- 
val. 

47° 

48° 

'? 

74 

10 
12i 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

5.837 
11.  674 
17.  511 
23.  318 
29.  185 
35.021 

49° 

24 

5 
7* 
10 
12| 

15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

5.838 
11.676 
17.  514 
23.352 
29.190 
35.027 

- 

49° 

50° 

'? 

74 

10 
12* 
15 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

Inches. 
0.001 
.002 
.005 
.008 
.013 
.019 

GEOGRAPHIC   TABLES    AND   FOEMULAS. 


77 


TABLE  9. — Coordinates  for  projection  of  maps  (scale 
[Prepared  by  S.  S.  Gannett.] 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

2*' 

5' 

7*' 

1(X 

15' 

Longitude 
interval. 

Inch. 

0             / 

25    00 
05 
07* 
10 
15 

20 
22* 
25 
30 

35 

% 

45 

50 
52* 
55 
60 

26    00 
05 
07* 
10 
15 

20 
22* 
25 
30 

35 

2 

45 

50 
52* 
55 
60 

27    00 
05 
07* 
10 
15 

20 
22* 
25 
30 

35 

S 

45 

50 
52* 
55 
60 

Inches. 
3.450. 
.448 
.446 
.445 
.443 

3.441 
.440 
.438 
.436 

3.434 
.433 
.431 
.429 

3.426 
.425 
.424 
.422 

3.422 
.419 
.418 
.417 
.414 

3.412 
.410 
.409 
.407 

3.405 
.403 
.402 
.'400 

3.397 
.396 
.394 
.392 

3.392 
.390 
.388 
.387 
.385 

3.382 
.380 
.379 
.377 

3.374 
.373 
.371 
.369 

3.367 
.365 
.364 
.361 

Inches. 
6.900 
.895 
.893 
.890 
.886 

6.881 
.879 
.876 
.872 

6.867 
.865 
.862 
.858 

6.852 
.850 
.848 
.843 

6.843 
.838 
.836 
.833 
.828 

6.824 
.821 
.819 
.814 

6.809 
.806 
.804 
.799 

6.794 
.792 
.789 
.784 

6.784 
.779 
.777 
'.774 
.769 

6.764 
.761 
.759 
.754 

6.749 
.746 
.743 
.738 

6.733 
.730 
.728 
.723 

Inches. 
10.350 
.343 
.339 
.336 
.329 

10.322 
.318 
.314 
.307 

10.300 
.297 
.293 
.286 

10.  279 
.276 
.272 
.264 

10.264 
.257 
.253 
.250 
.243 

10.236 
.232 
.238 
.221 

10.  214 
.210 
.206 
.198 

10.  191 
.188 
.184 
.176 

10.  177 
.169 
.165 
.161 
.153 

10.  146 
.142 
.138 
.131 

10.  124 
.120 
.116 
.108 

10.100 
.095 
.092 
.084 

Inches. 
13.800 
.790 
.786 
.781 
.772 

13.772 
.758 
.753 
.744 

13.  734 
.730 
.725 
.715 

13.705 
.700 
.696 
.686 

13.686 
.677 
.672 
.666 
.657 

13.647 
.642 
.638 
.628 

13.  618 
.612 
.608 
.598 

13.588 
.583 
.578 
.569 

13.569 
.559 
.554 
.548 
.538 

13.  528 
.523 
.518 
.508 

13.  498 
.492 

.487 
.477 

13.  467 
.461 
.456 
.446 

Inches. 
20.700 
.685 
.678 
.671 
.657 

20.643 
.636 
.629 
.615 

20.601 
.594 
.587 
.573 

20.  558 
.551 
.544 
.529 

20.529 
.514 
.506 
.499 
.485 

20.  471 
.464 
.457 
.442 

20.427 
.419 
.412 
.397 

20.382 
.375 
.367 
.353 

20.353 
.338 
.330 
.322 
.307 

20.292 

.284 
.277 
.262 

20.  247 
.239 
.231 
.215 

20.200 
.191 
.184 
.169 

/ 
5 
71 

10 
15 

0.002 
.005 
.008 
.019 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.514 
3.028 
4.542 
6.057 
7.571 
9.085 
10.599 
12.  114 
13.  628 
15.142 

Longitude 
interval. 

Inch. 

5 

.? 

15 

0.002 
.005 
.009 
.020 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 

4 
5 
6 
7 
8 
9 
10 

Inches. 
1.515 
3.029 
4.544 
6.058 
7.573 
9.  087 
10.602 
12.  115 
13.  631 
15.  145 

Longitude 
interval. 

Inch. 

5 

,? 

15 

0.002 
.005 
.009 
.020 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.515 
3.029 
4.  544 
6.058 
7.574 
9.087 
10.603 
12.  117 
13.  632 
15.  147 

«  This  table  can  be  used  for  even  multiples  or  divisions  of  the  y^A™  scale,  as  indicated  in  the  two  fol- 
lowing cases.  Scale  Mtaj,:  For  a  given  latitude  the  meridional  distance  for  a  certain  latitude  inter- 
val and  the  abscissas  and  ordinates  for  a  certain  longitude  interval  are  double  the  values  given  in  the 
table.  Scale  5Bij»j:  For  a  given  latitude  the  meridional  distance  for  a  certain  latitude  interval  and 
the  abscissas  and  ordinates  for  a  certain  longitude  interval  are  half  the  values  given  in  the  table. 


78 


GEOGRAPHIC   TABLES    AND    FORMULAS. 


TABLE  9. — Coordinates  for  projection  of  maps  (scale  53-^) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

2*' 

5' 

71' 

10' 

15' 

Longitude 
interval. 

Inch. 

0              / 

28    00 
05 
07J 
10 
15 

20 
22| 
25 
30 

35 

% 

45 

50 
52J 
55 
60 

29    00 
05i 
07 
10 
15 

20 
22J 
25. 
30 

35 

I" 

45 

50 
52* 
55 
60 

30    00 
05 
07i 
10 
15 

20 
22| 
25 
30 

35 

® 

45 
50 

SJ 

60 

Inches. 
3.361 
.359 
.357 
.356 
.354 

3.352 
.350 
.349 
.346 

3.343 
.342 
.340 
.338 

3.336 
.334 
.333 
.330 

3.330 
.328 
.326 
.325 
.322 

3.319 
.318 
.317 
.314 

3.311 
.310 
.309 
.305 

3.303 
.302 
.300 
.298 

3.298 
.295 
.294 
.292 
.289 

3.286 
.285 
.284 
.281 

3.278 
.277 
.275 
.273  . 

3.270 
.268 
.267 
.264 

Inches. 
6.723 
.718 
.715 
.713 
.708 

6.703 
.700 
.698 
.692 

6.687 
.684 
.681 
.676 

6.671 
.668 
.666 
.660 

6.660 
.655 
.652 
.649 
.644 

6.638 
.636 
.633 
.628 

6.622 
.620 
.617 
.611 

6.605 
.603 
.600 
.595 

6.595 
.590 

.587 
.584 
.578 

6.572 
.570 
.567 
.562 

6.556 
.553 
.550 
.545 

6.540 
.537 
.534 
.528 

Inches. 
10.084 
.077 
.072 
.069 
.061 

10.054 
.050 
.046 
.038 

10.  030 
.026 
.022 
.014 

10.006 
.002 
9.998 
.990 

9.990 
.982 
.978 
.974 
.966 

9.958 
.954 
.950 
.942 

9.934 
.930 
.925 
.916 

9.908 
.904 
.900 
.892 

9.892 

.884 
.880 
.876 
.867 

9.858 
.855 
.850 
.842 

9.824 
.830 
.826 
.818 

9.810 
.805 
.801 
.792 

Inches. 
13.  446 
.436 
.430 
.425 
.415 

13.405 
.400 
.395 
.384 

13.  373 
.368 
.363 
.352 

13.342 
.336 
.331 
.320 

13.  320 
.310 
.304 
.299 
.288 

13.277 
.271 
.266 
.255 

13.  245 
.239 
.234 
.222 

13.  211 
.206 
.200 
.190 

13.190 
.179 
.173 
.168 
.156 

13.  145 
.140 
.134 
.123 

13.  112 
.106 
.101 
.090 

13.080 
.074 
.068 
.056 

Inches. 
20.  169 
.154 
.145 
.138 
.123 

20.  108 
.100 
.092 
.076 

20.060 
.052 
.044 
.028 

20.013 
.005 
19.  997 
.981 

19.  980 
.964 
.956 
.948 
.932 

19.  915 
.907 
.899 
.883 

19.867 
.859 
.850 
.833 

19  816 
.808 
.800 
.785 

19.  785 
.768 
.760 
.751 
.734 

19.  717 
.710 
.701 
.685 

19.668 
.659 
.651 
.635 

19.  619 
.611 
.602 
.584 

5 

-  i? 

15 

0.002 
.005 
.009 
.021 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.515 
3.030 
4.545 
6.060 
7.575 
9.090 
10.605 
12.  120 
13.635 
15.150 

Longitude 
interval. 

Inch. 

f 

5 

i? 

15 

0.002 
.005 
.009 
.021 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
*7 
8 
9 
10 

Inches. 
1.515 
3.030 
4.545 
6.060 
7.575 
9.090 
10.605 
12.122 
13.637 
15.  152 

Longitude 
interval. 

Inch. 

5 

7| 
10 
15 

0.002 
.005 
.009 
.021 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.515 
3.030 
4.545 
6.061 
7.576 
9.092 
10.608 
12.  123 
13.638 
15.154 

GEOGRAPHIC  TABLES  AND  FORMULAS. 

L-. 

TABLE  9. — Coordinates  for  projection  of  maps  (scale  ?J%-Q-Q) — Continued. 


79 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

W 

5' 

7|' 

10' 

15' 

Longitude 
interval. 

Inch. 

0            / 

31    00 
05 
07* 
10 
15 

20 

8* 

30 
35 

3^ 

45 

-       50 
52i 
55 
60 

32    00 
05 
07* 
10 
15 

20 
22J 
25 
30 

35 

3<? 

45 

50 
52* 
55 
60 

33    00 
05 
07* 
10 
15 

20 
22* 
25 
30 

35 

£4 

45 
50 

1J 

60 

Inches. 
3.264 
.261 
.259 
.258 
.256 

3.253 
.251 
.250 
.247 

3.244 
.243 
.241 
.239 

3.236 
.234 
.233 
.230 

3.230 
.227 
.225 
.223 
.220 

3.218 
.216 
.214 
.212 

3.208 
.207 
.205 
.202 

3.200 
.198 
.197 
.194 

3.194 
.191 
.190 
.188 
.185 

3.182 
.180 
.178 
.176 

3.172 
.171 
.169 
.166 

3.163 
.162 
.160 
.157 

Inches. 
6.528 
.522 
.519 
.517 
.511 

6.505 
.502 
.499 
.494 

6.488 
.485 
.482 
.477 

6.471 
.468 
.465 
.459 

6.459 
.453 
.450 
.447 
.441 

6.435 
.432 
.429 
.423 

6.417 
.414 
.411 
.405 

6.400 
.396 
.393 
.387 

6.387 
.382 
.379 
.376 
.370 

6.364 
.360 
.357 
.351 

6.345 
.342 
.339 
.333 

6.327 
.324 
.320 
.314 

Inches. 
9.792 
.783 
.779 
.775 
.766 

9.757 
.753 
.749 
.741 

9.732 
.728 
.723 
.715 

9.707 
.702 
.697 
.688 

9.688 
.680 
.675 
.670 
.661 

9.652 
.648 
.644 
.635 

9.625 
.621 
.617 
.608 

9.600 
.595 
.590 
.581 

9.581 
.572 
.568 
.563 
.554 

9.545 
.540 
.536 
.527 

9.517 
.513 
.508 
.499 

9.490 
.485 
.481 
.472 

Inches. 
13.056 
.044 
.039 
.033 
.022 

13.  010 
.004 
12.999 
.988 

12.976 
.970 
.964 
.953 

12.  942 
.936 
.930 
.918 

12.  918 
.906 
.900 
.894 
.882 

12.  870 
.864 
.858T 
.846. 

12.834 
.828 
.822 
.811 

12.799 
.793 
.787 
.775 

12.  775 
.763 
.757 
.751 
.739 

12.  727 
.720 
.714 
.702 

12.690 
.684 
.678 
.665 

12.653 
.647 
.641 
.629 

Inches. 
19.584 
.567 
.558 
.550 
.533 

19.  515 
.506 
.498 
.481 

19.464 
.455 
.447 
.430 

19.  413 
.404 
.395 
.377 

19.  377 
.359 
.350 
.341 
.323 

19.305 
.296 
.287 
.269 

19.  251 
.242 
.233 
.216 

19.199 
.189 
.180 
.162 

19.  162 
.145 
.136 
.127 
.109 

19.090 
.080 
.071 
.053 

19.035 
.026 
.017 
18.998 

18.980 
.971 
.961 
.943 

5 

2 

15 

0.002 
.005 
.010 
.022 

Latitude, 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.515 
3.031 
4.545 
6.062 
7.578 
9.093 
10.609 
12.  124 
13.640 
15.  156 

Longitude, 
interval. 

Inch. 

5 

i? 

15 

0.002 
.006 
.010 
.022 

Latitude 
interval. 

Meridional 
distance. 

/ 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.516 
3.032 
4.547 
6.063 
7.579 
9.095 
10.  611 
12.  127 
13.643 
15.  159 

Longitude 
interval. 

Inch. 

5 

2 

15 

0.003 
.006 
.010 
.023 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.516 
3.032 
4.548 
6.065 
7.580 
9.097 
10.  613 
12.129 
13.645 
15.  161 

80 


GEOGRAPHIC  TABLES  AND  FORMULAS 


TABLE  9. — Coordinates  for  projection  of  maps  (scale  ^ozr) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

W 

5' 

7|' 

.10' 

15' 

Longitude 
interval. 

Inch. 

0           / 

34    00 
05 
07J 
10 
15 

20 
22J 
25 
30 

35 

S1 

45 

50 
52£ 
55 
60 

35    00 
05 
07£ 
10 
15 

20 
22i 
25" 
30 

35 
37i 
40 
45 

50 
52£ 
55 
60 

36    00 
05 
07£ 
10 
15 

20 
22J 
25 
30 

35 
37 
40 
45 

50 
52 
55 
60 

Inches. 
3.157 
.154 
.152 
.151 
.148 

3.145 
.143 
.142 
.139 

3.135 
.134 
.132 
.129 

3.126 
.124 
.123 
.120 

3.120 
.117 
.115 
.114 
.110 

3.107 
.105 
.104 
.100 

3.097 
.096 
.094 
.091 

3.088 
.086 
.084 
.082 

3.082 
.078 
.076 
.075 
.072 

3.068 
.067 
.065 
.062 

3.058 
.057 
.055 
.052 

3.048 
.047 
.045 
.042 

Inches. 
6.314 
.309 
.305 
.302 
.296 

6.290 
.286 
.283 

.277 

6.271 

.268 
.26J 
.258 

6.252 
.249 
.246 
.240 

6.240 
.233 
.230 
.227 
.220 

6.214 
.211 

.208 
.201 

6.195 
.192 
.188 
.182 

6.176 
.172 
.169 
.163 

6.163 
.156 
.153 
.150 
.144 

6.137 
.134 
.130 
.124 

6.117 
.114 
.110 
.104 

6.097 
.094 
.091 
.084 

Inches. 
9.472 
.462 
.457 
.453 
.444 

9.434 
.430 
.425 
.416 

9.406 
.402 
.396 
.387 

9.378 
.374 
.369 
.360 

9.360 
.350 
.345 
.340 
.330 

9.321 
.317 
.312 
'.302 

9.292 
.288 
.283 
.273 

9.263 
.258 
.254 
.244 

9.244 
.234 
230' 
.225 
.215 

9.205 
.200 
.195 
.185 

9.176 
.171 
.166 
.156 

9.146 
.141 
.136 
.126 

Inches. 
12.629 
.617 
.610 
.604 
.592 

12.  579 
.572 
.567 
.554 

12.542 
.535 
.529 
.517 

12.504 
.498 
.492 
.479 

12.  479 
.466 
.460 
.454 
.441 

12.428 
.422 
.415 
.402 

12.390 
.384 
.377 
.364 

12.  351 
.345 
.338 
.326 

12.  326 
.313 
.306 
.300 

.287 

12.  274 
.268 
.260 
.247 

12.  234 

.228 
.221 
.208 

12.  194 
.188 
.182 
.169 

Inches. 
18.  943 
.925 
.915 
.906 
.888 

18.  869 
.859 
.850 
.831 

18.  813 
.803 
.793 
.775 

18.756 
.747 
.738 
.719 

18.  719 
.699 
.690 
.681 
.661 

18.642 
.633 
.623 
.604 

18.585 
.576 
.565 
.546 

18.  527 
.517 
.508 
.489 

18.489 
.469 
.459 
.450 
.431 

18.  411 
.401 
.390 
.371 

18.  351 
.342 
.332 
.312 

18.292 
.282 
.272 
.253 

/ 

5 

$ 

15 

0.003 
.006 
.010 
.023 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.516 
3.032 
4.548 
6.065 
7.581 
9.096 
10.  613 
12.  130 
13.646 
15.  162 

Longi- 
tude 
interval. 

Inch. 

5 
7J 

10 
15 

0.003 
.006 
.010 
.023 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.516 
3.033 
4.549 
6.067 
7.583 
9.100 
10.  616 
12.  133 
13.  648 
15.  164 

Longi- 
tude 
interval. 

Inch. 

5 

i? 

15 

0.003 
.006 
.010 
.024 

Latitude 
interval. 

Meridional 
distance. 

1 

2 
3 
4 
5 
,6 
7 
8 
9 
10 

Inches. 
1.517 
3.034 
4.551 
6.067 
7.584 
9.102 
10.  619 
12.  135 
13.652 
15.  169 

GEOGRAPHIC   TABLES    AND   FORMULAS. 


81 


TABLE  9. — Coordinates  for  projection  of  maps  (scale  53-^7) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

w 

5' 

7*' 

10' 

15' 

Longitude 
interval. 

Inch. 

0            / 

37    00 
05 
07| 
10 
15 

20 

1> 

30 
35 

% 

45 
50 

S1 

60 

38    00 
05 
07* 
10 
15 

20 

% 

30 

35 
37* 
40 
45 

50 

s? 

60 

39    00 
05 
07i 
10 
15 

20 

9 

30 
35 

% 

45 

50 
52J 
55 
60 

Inches. 
3.042 
.038 
.037 
.035 
.032 

3.028 
.027 
.024 
.022 

3.019 
.017 
.015 
.012 

3.009 
.006 
.005 
.001 

3.001 
2.998 
.997 
.995 
.991 

2.988 
.987 
.984 
.981 

2.978 
.976 
.974 
.971 

2.968 
.966 
.964 
.960 

2.960 
.957 
.955 
.954 
.950 

2.946 
.945 
.943 
.940 

2.936 
.934 
.933 
.929 

2.926 
.924 
.922 
.919 

Inches. 
6.084 
.077 
.074 
.070 
.064 

6.057 
.053 
.049 
.044 

6.037 
.034 
.030 
.024 

6.017 
.013 
.010 
.003 

6.003 
5.996 
.993 
.990 
.983 

5.976 
.973 
.969 
.962 

5.955 
.952 
.949 
.942 

5.935 
.932 
.928 
.921 

5.921 
.914 
.910 
.907 
.900 

5.893 
.890 
.886 
.879 

5.872 
.868 
.865 
.858 

5.851 
.848 
.844 
.837 

Inches. 
9.126 
.116 
.111 
.106 
.096 

9.086 
.081 
.076 
.066 

9.056 
.051 
.045 
.035 

9.025 
.020 
.015 
.004 

9.004 
8.994 
.989 
.984 
.974 

8.964 
.959 
.954 
.944 

8.933 
.927 
.923 
.913 

8.902 
.897 
.892 
.882 

8.882 
.871 
.865 
.860 
.850 

8.840 
.835 
.829 
.819 

8.808 
.802 
.798 

.787 

8.777 
.772 
.766 
.755 

Inches. 
12.  169 
.155 
.148 
.141 
.128 

12.  114 
.107 
.101 
.088 

12.  074 
.068 
.061 
.048 

12.034 
.027 
.020 
.006 

12.006 
11.993 
.986 
.980 
.966 

11.  952 
.946 
.939 
.925 

11.  911 
.904 
.898 
.884 

11.  870 
.863 
.856 
.842 

11.842 
.828 
.821 
.814 
.800 

11.786 
.779 
.772 
.758 

11.  744 
.737 
.730 
.716 

11.  702 
.695 
.688 
.674 

Inches. 
18.253 
.232 
.222 
.212 
.192 

18.  172 
.162 
.152 
.132 

18.112 
.102 
.091 
.071 

18.050 
.040 
.030 
.009 

18.009 
17.  989 
.979 
.969 
.949 

17.929 
.919 
.908 
.887 

17.867 
.856 
.846 
.826 

17.805 
.795 
.784 
.763 

17.  763 
.742 
.731 
.721 
.700 

17.679 
.669 
.658 
.637 

17.  616 
.605 
.595 
.574 

17.553 
.543 
.532 
.511 

5 

,? 

15 

0.003 
.006 
.010 
.024 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.517 
3.034 
4.551 
6.068 
7.585 
9.102 
10.  619 
12.  136 
13.653 
15.  170 

Longi- 
tude 
interval. 

Inch. 

5 

'i? 

15 

0.003 
.006 
.010 
.024 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.517 
3.034 
4.551 
6.069 
7.586 
9.103 
10.  620 
12.138 
13.655 
15.  172 

Longi- 
tude 
interval. 

Inch. 

5 

i? 

15 

0.003 
.006 
.011 
.024 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.517 
3.035 
4.552 
6.070 
7.587 
9.105 
10.  622 
12.  140 
13.658 
15.  175 

46061—08 6 


82  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  9. — Coordinates  for  projection  of  maps  (scale  ^^o) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

V 

5' 

74' 

10' 

15' 

Longitude 
interval. 

Inch. 

40    00 

2.919 

5.837 

8.755 

11.674 

17.  5M 

5 

0.003 

05 

.915 

.830 

.745 

.660 

.490 

71 

.006 

074 

.913 

.826 

.740 

.653 

.479 

10 

.011 

10 

.912 

.823 

.734 

.646 

.469 

15 

.024 

15 

.908 

.816 

.723 

.631 

.447 

Latitude 

Meridional 

20 

2.904 

5.808 

8.712 

11.  616 

17.  424 

interval. 

distance. 

22X 

902 

804 

706 

.609 

413 

AAg 

25 

.900 

.801 

.702 

.602 

.403 

, 

Inches. 

30 

.897 

.794 

.691 

.588 

.382 

1 

1.518 

2 

3.  035 

3 

4.557 

35i 

2.894 

5.787 

8.680 

11.574 

17.  361 

4 

6.070 

.892 

.784 

.675 

.567 

.351 

5 

7.588 

40 

.890 

.780 

.670 

.560 

.340 

6 

9.106 

45 

.886 

.772 

.659 

.545 

.317 

7 

10.  624 

8 

12.  143 

9 

13.  660 

50 

2.883 

5.765 

8.648 

11.530 

17.295 

10 

15.  178 

§* 

.881 

.762 

.642 

.523 

.285 

55 

60 

.  879 
.875 

.  758 
.750 

.  636 
.625 

.  516 
.501 

.  273 
.251 

Longitude 
interval. 

Inch. 

41     00 

2.875 

5.750 

8.625 

11.501 

17.  251 

, 

05 

.872 

.743 

.614 

.486 

.229 

5 

0.003 

074 

.870 

.740 

.609 

.479 

.219 

7i 

.006 

10 

.868 

.736 

.604 

.472 

.208 

10 

.011 

15 

.864 

.729 

.594 

.458 

.187 

15 

.025 

20 
224 
25 

2.861 
.859 

.857 

5.722 
.718 
.714 

8.582 
.577 
.572 

11.  443 
.436 

.428 

17.  165 
.154 
.143 

Latitude 
interval. 

Meridional 
distance. 

30 

.854 

.707 

.561 

.414 

.121 

/ 

Inches. 

1 

1.518 

35 

ff 

45 

2.850 
.848 
.846 
.843 

5.700 
.696 
.692 
.685 

8.550 
.544 
.539 
.528 

11.399 
.392 
.385 
.370 

17.099 
.088 
.077 
.055 

2 
3 
4 
5 
6 

3.036 
4.554 
6.072 
7.590 
9.108 

7 

10.626 

50 
524 
55 
60 

2.839 
.837 
.835 
.831 

5.678 
.674 
.670 
.663 

8.517 
.510 
.505 
.494 

11.355 
.347 
.340 
.326 

17.  033 
.021 
.011 
16.  989 

8 
9 
10 

12.  145 
13.663 
15.  181 

42    00 

2.831 

5.663 

8.494 

11.  326 

16.  989 

Longitude 
interval. 

" 

Inch. 

05 

.827 

.655  ' 

.483 

.311 

.966 

074 
10 

.826 
.824 

.652 
.648 

.478 
.472 

.304 
.296 

.956 
.944 

5 

71 

0.003 

fVlfi 

15 

.820 

.641 

.462 

.282 

.923 

'§ 

10 

.  UUD 

.011 

15 

.025 

20 

2  817 

5  634 

8  450 

11  267 

16  901 

224 
25 
30 

!sis 

.813 
.809 

.630 
.626 
.618 

!444 
.439 
.428 

.259 
.252 
.237 

.889 
.878 
.855 

Latitude 
interval. 

Meridional 
distance. 

/ 

Inches. 

35 

2.805 

5.611 

8.417 

11.222 

16.833 

1 

1.518 

.804 

.608 

.412 

.215 

.823 

2 

3.036 

40 

.802 

.604 

.406 

.208 

.812 

3 

4.554 

45 

.798 

.597 

.395 

.192 

.790 

4 

5 

6.073 
7.591 
o  ino 

50 

2.794 

5.589 

8.384 

11.  178 

16.  767 

7 

y»  ii/y 
10.  627 

524 
55 
60 

.793 
.791 

.787 

.585 
.582 
.574 

.378 
.372 
.361 

.170 
.163 
.148 

.755 
.745 
.722 

8 
9      . 
10 

12.  147 
•      13.666 
15.  184 

GEOGRAPHIC  TABLES  AND  FORMULAS. 


83 


TABLE  9.  —  Coordinates  for  projection  of  maps  (scale 


—  Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

2J' 

5' 

7!' 

10' 

15' 

Longitude 
interval. 

Inch. 

0          / 

43  -00 
05 
07J 
10 
15 

20 

1* 

30 
35 

J? 

45 

50 
52J 
55 
60 

44    00 
05 
07J 
10 
15 

20 

f 

30 
35 

$ 

45 

50 
52£ 
55 
60 

45    00 
05 
07* 
10 
15 

20 

1* 

30 
35 

% 

45 

50 
52| 
55 
60 

Inches. 

2.787 
.783 
.781 
.779 
.776 

2.772 
.770 
.768 
.764 

2.760 
.758 
.756 
.752 

2.749 
.747 
.745 
.741 

2.741 
.737 
.735 
.733 
.730 

2.726 
.723 
.722 
.718 

2.714 
.712 
.710 
.706 

2.702 
.700 
.698 
.695 

2.695 
.691 
.689 
.687 
.683 

2.679 
.677 
.675 
.671 

2.667 
.665 
.663 
.660 

2.655 
.654 
.652 
.648 

Inches. 
5.574 
.566 
.562 
.558 
.551 

5.543 
.539 
.535 
.528 

5.520 
.516 
.512 
.505 

5.498 
.494 
.490 
.482 

5.482 
.474 
.470 
.467 
.459 

5.451 
.447 
.444 
.436 

5.428 
.424 
.420 
.413 

5.405 
.401 
.397 
.390 

5.390 
.382 
.378 
.374 
.366 

5.358 
.354 
.350 
.342 

5.334 
.330 
.326 
.319 

5.311 
.307 
.303 
.295 

Inches. 
8.361 
.349 
.343 
.338 
.326 

8.314 
.308 
.303 
.292 

8.280 
.274 
.268 
.257 

8.246 
.240 
.235. 
.223 

8.223 
.212 
.206 
.200 
.188 

8.177 
.171 
.166 
.154 

8.142 
.136 
.130 
.119 

8.108 
.102 
.096 
.084 

8.084 
.073 
.067 
.061 
.049 

8.038 
.032 
.026 
.014 

8.002 
7.996 
.990 
.978 

7.966 
.960 
.954 
.942 

Inches. 
11.148 
.132 
.124 
.117 
.102 

11.086 
.078 
.070 
.055 

11.040 
.032 
.025 
.010 

10.995 
.987 
.980 
.964 

10.964 
.949 
.941 
.934 
.918 

10.902 
.894 
.887 
.872 

10.856 

.848 
.840 
.825 

10.810 
.802 
.794 
.779 

10.  779 
.764 
.756 
.748 
.732 

10.717 
.708 
.701 
.685 

10.669 
.661 
.653 
.638 

10.622 
.614 
.606 
.590 

Inches. 
16.  722 
.698 
.686 
.675 
.653 

16.629 
.617 
.606 
.583 

16.560 
.548 
.537 
.515 

16.  493 
.481 
.470 
.446 

16.  446 
.423 
.411 
.400 
.377 

16.354 
.341 
.331 
.308 

16.284 
.272 
.261 
.238 

16.215 
.203 
.192 
.169 

16.  169 
.146 
.134 
.122 
.098 

16.075 
.063 
.051 
.027 

16.003 
15.991 
.980 
.957 

15.933 
.921 
.909 

.885 

5 

•? 

15 

0.003 
.006 
.011 
.025 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 
4 
5 
6 

8 
9 
10 

Inches. 
1.519 
3.038 
4.557 
6.075 
7.594 
9.113 
10.631 
12.  149 
13.668 
15.  187 

Longitude 
interval. 

Inch. 

5 

,? 

15 

0.003 
.006 
.011 
.025 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3 

4 
5 
6 

7 
8 
9 
10 

Inches. 
1.519 
3.038 
4.557 
6.076 
7.595 
9.114 
10.  633 
12.152 
13.  671 
15.  190 

Longitude 
interval. 

Inch. 

5 

$ 

15 

0.003 
.006 
.011 
.025 

Latitude 
interval. 

Meridional 
distance. 

1 

2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.519 
3.038 
4.557 
6.077 
7.596 
9.115 
10.635 
12.  154 
13.673 
15.  192 

84 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  9. — Coordinates  for  projection  of  maps  (scale  ^5-^^) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

2J' 

5' 

7¥ 

10' 

15' 

Longitude 
interval. 

Inch. 

0           / 

46    00 
05 
07^ 
10 
15 

20 
22J 
25 
30 

35 

5? 

45 

50 
52J 
55 
60 

47    00 
05 
07i 
10 
15 

20 
22 
25 
30 

35 
37J 
40 
45 

50 
52* 
55 
60 

48    00 
05 
07£ 
10 
15 

20 
22J 
25 
30 

35 

5? 

45 

50 
52J 
55 
.      60 

Inches. 
2.648 
.644 
.640 
.639 
.635 

2.631 
.630 
.627 
.623 

2.619 
.617 
.615 
•.611 

2.607 
.605 
.603 
.599 

2.599 
.595 
.593 
.591 
.587 

2.583 
.581 
.579 
.575 

2.570 
.568 
.567 
.563 

2.559 
.557 
.555 
.550 

2.550 
.546 
.544 
.542 
.538 

2.534 
.532 
.530 
.526 

2.522 
.520 
.517 
.513 

2.509 
.507 
.505 
.501 

Inches. 
5.295 
.287 
.281 
.279 
.271 

5.263 
.259 
.255 
.247 

5.239 
.235 
.230 
.223 

5.214 
.210 
.206 
.198 

'     5.198 
.190 
.186 
.182 
.174 

5.166 
.162 
.158 
.150 

5.141 
.137 
.133 
.125 

5.117 
.113 
.109 
.100 

5.100 
.092 
.088 
.084 
.076 

5.068 
.064 
.060 
.051 

5.043 
.039 
.034 
.026 

5.018 
.014 
.010 
.002 

Inches. 
7.942 
.930 
.922 
.918 
.906 

7.894 
.888 
.882 
.870 

7.858 
.852 
.846 
.834 

7.822 
.816 
.810 
.798 

7.798 
.786 
.780 
.774 
.761 

7.749 
.743 
.737 
.724 

7.712 
.706 
.700 
.688 

7.676 
.670 
.663 
.650 

7.650 
.638 
.632 
.626 
.614 

7.602 
.596 
.590 
.577 

7.564 
.558 
.552 
.539 

7.527 
.521 
.515 
.502 

Inches. 
10.590 
.574 
.562 
.558 
.542 

10.  526 
.518 
.510 
.494 

10.  478 
.470 
.461 
.445 

10.  429 
.421 
.413 
.397 

10.  397 
.381 
.373 
.365 
.348 

10.332 
.324 
.316 
.299 

10.  282 
.274 
.266 
.250 

10.  234 
.226 
.218 
.201 

10.201 
.185 
.177 
.168 
.152 

10.136 
.128 
.119 
.102 

10.  086 
.078 
.069 
.052 

10.036 
.028 
.020 
.003 

Inches. 
15.885 
.861 
.844 
.837 
.813 

15.  789 
.777 
.765 
.741 

15.  717 
.705 
.692 
.667 

15.  643 
.631 
.619 
.595 

15.  595 
.571 
.559 
.547 
.522 

15.  498 
.486 
.474 
.449 

15.  423 
.411 
.399 
.375 

15.351 
.339 
.326 
.307 

15.  301 
.277 
.265 
.252 
.228 

15.  204 
.192 
.179 
.154 

15.  129 
.116 
.103 
.078 

15.  054 
.042 
.030 
.005 

5 

i? 

15 

0.003 
.006 
.011 
.025 

Latitude 
interval. 

Meridional 
distance. 

1 
2 
3. 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.520 
3.039 
4.559 
6.078 
7.598 
9.117 
10.637 
12.  157 
13.  677 
15.196 

Longitude 
interval. 

Inch. 

5 

i? 

15 

0.003 
.006 
.011 
.025 

Latitude 
interval. 

Meridional 
distance. 

/ 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Inches. 
1.520 
3.039 
4.559 
6.079 
7.599 
9.119 
10.638 
12.  158 
13.  678 
15.  197 

Longitude 
interval. 

Inch. 

5 

i? 

15 

0.003 
.006 
.011 
.025 

Latitude 
interval. 

Meridional 
distance. 

1 

2 
3 

4 
5 
6 
7 
8 
9 
10 

Inches. 
1.520 
3.04) 
4.560 
6.080 
7.600 
9.120 
10.  640 
12.160 
13.680 
15.200 

GEOGRAPHIC  TABLES  AND  FORMULAS. 


85 


TABLE  9. — Coordinates  for  projection  of  maps  (scale 


) — Continued. 


Abscissas  of  developed  parallel. 

Ordinates  of  devel- 

Latitude 
ol 

Longitude  interval. 

oped  parallel. 

parallel. 

*§' 

5' 

7*' 

lO' 

15' 

Longitude 
interval. 

Inch. 

0             / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

/ 

49    00 

2.501 

5.002 

7.502 

10.003 

15.005 

5 

0.003 

05 

2.496 

4.993 

.490 

9.986 

14.980 

7J 

.006 

07J 

.494 

.989 

.484 

.978 

.967 

10 

.011 

10 

.492 

.985 

.477 

.970 

.955 

15 

.025 

15 

.488 

.976 

.464 

.952 

.929 

Latitude 

Meridional 

20 

2.484 

4.968 

7.452 

9.936 

14.904 
ono 

interval. 

distance. 

% 

.  482 
.480 

.  964 
.960 

.  446 
.440 

.  928 
.920 

.  o\)Z 
.880 

/ 

Inches. 

30 

.476 

.952 

.428 

.903 

.855 

1 

1.520 

2 

3.040 

3 

4.560 

35 

2.472 

4.943 

7.415 

9.886 

14.829 

4 

6.081 

37J 

.470 

.939 

.408 

.878 

.816 

5 

7.601 

40 

.467 

.934 

.402 

.869 

.803 

6 

9.121 

45 

.463 

.926 

.389 

.852 

.778 

7 

10.  641 

8 

12.  162 

9 

13.682 

50 

2.459 

4.918 

7.377 

9.836 

14.  754 

10 

15.202 

52i 

.457 

.914 

.371 

.828 

.742 

55 

.455 

.910 

.364 

.819 

.729 

60 

.450 

.901 

.352 

.802 

.703 

86  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  T 
[Prepared  by  S.  S.  Gannett  and  George  T.  Hawkins.] 


Abscissas  of  developed  parallel. 

Ordinates  of  devel- 

Latitude 
of 

oped  parallel. 

Longitude  interval. 

parallel. 

1'. 

2'. 

3'. 

4'. 

5'. 

Longi- 
tude 

Inch. 

interval. 

o     / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

, 

25    00 

5.520 

11.040 

16.  560 

22.  080 

27.600 

1 

.000 

05 

.516 

.032 

.549 

.065 

.581 

2 

.002 

07* 

.515 

.029 

.544 

.057 

.572 

3 

.003 

10 

.512 

.025 

.538 

.050 

.562 

4 

.006 

15 

.509 

.018 

.528 

.035 

.544 

5 

.009 

20 
25S 

5.505 
.503 
.501 

11.  010 
.006 
.002 

16.  515 
.509 
.503 

22.  020 
.012 
.005 

27.  525 
.516 
.506 

Latitude 
interval. 

Meridi- 
onal 
distance 

30 

.497 

10.995 

.492 

21.990 

.487 

i 

Inches. 

1 

6.057 

35 

5.494 

10.988 

16.  480 

21.  975 

27.468 

2 

12.  114 

37* 
40 
45 

.492 
.490 
.486 

.984 
.980 
.972 

.476 
.470 
.458 

.968 
.960 
.945 

.459 
.449 
.430 

3 
4 
5 

18.  171 
24.228 
30.285 

50 

5  482 

10  965 

16.  448 

2i  930 

27  411 

52* 

!480 

!921 

!401 

Longi- 

55 

.478 

!957 

!435 

.915 

.392 

tude 

Inch. 

60 

.475 

.950 

.424 

.900 

.373 

interval. 

26  .00 

5.475 

10.950 

16.  424 

21.900 

27.  373 

1 

.000 

05 

.470 

.942 

.412 

.882 

.353 

2 

.  002 

07* 

.469 

.937 

.406 

.875 

.343 

3 

10 

.467 

.933 

.400 

.867 

.333 

4 

006 

15 

.463 

.925 

.389 

.852 

.314 

5 

'.009 

20 
25* 

5.459 
.457 
.455 

10.  918 
.914 
.910 

16.  377 
.371 
.365 

21.835 
.828 
.820 

27.294 
.284 
.275 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.451 

.902 

.353 

.805 

.255 

/ 

Inches. 

1 

6.058 

35 

5.447 

10.894 

16.  341 

21.  789 

27.235 

2 

12.  115 

37* 

.445 

.890 

.335 

.780 

.225 

3 

18.  173 

40 

.443 

.887 

.330 

.773 

.216 

4 

24.231 

45 

.439 

.878 

.318 

.758 

.196 

5 

30.  289 

50 

5.435 

10.  870 

16.306 

21.  741 

27.  176 

52- 

.433 

.866 

.298 

.732 

.167 

Longi- 

55* 

.431 

.863 

.294 

.725 

.157 

tude 

Inch. 

60 

.428 

.855 

.282 

.710 

.138 

interval. 

27    00 

5.428 

10.855 

16.  283 

21.  710 

27.138 

1 

.000 

05 

.422 

.848 

.270 

.695 

.118 

2 

.002 

07* 

.421 

.843 

.264 

.686 

.108 

3 

.003 

10 

.420 

.839 

.258 

.678 

.097 

4 

.006 

15 

.415 

.831 

.247 

.662 

.077 

5 

.010 

20 
22* 
25 

5.410 
.409 
.407 

10.822 
.818 
.815 

16.233 
.227 
.220 

21.645 
.636 
.628 

27.056 
.046 
.035 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.403 

.805 

.210 

.612 

.015 

/ 

Inches. 

1 

6.058 

35  , 

5.399 
.397 

10.  798 
.794 

16.  198 
.191 

21.595 

.588 

26.995 
.984 

2 
3 

12.  117 
18.  175 

405 
45 

.395 
.391 

.790 
.782 

.185 
.172 

.580 
.562 

.974 
.953 

4 
5 

24.235 
30.292 

50 

5.387 

10.  774 

16.160 

21.548 

26.  933 

52i 

.384 

.768 

.154 

.538 

.922 

55° 

.382 

.765 

.148 

.530 

.912 

60 

.378 

.758 

.135 

.515 

.892 

GEOGRAPHIC  TABLES  AND  FORMULAS.  87 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  TT^rnr) — Continued. 


Abscissas  of  developed  parallel. 

Ordinates  of  devel- 

Latitude 
of 

oped  parallel. 

Longitude  interval. 

parallel. 

Longi- 

1'. 

2'. 

3'. 

4'. 

5'. 

tude 

Inch. 

interval. 

o     / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

, 

28    00 

5.378 

10.758 

16.135 

21.515 

26.  892 

1 

.000 

05 

.374 

.749 

.122 

.498 

.871 

2 

.002 

071 

.372 

.745 

.116 

.488 

.861 

3 

.003 

10 

.370 

.740 

.110 

.480 

.850 

4 

.006 

15 

.366 

.732 

.098 

.465 

.830 

5 

.010 

20 
221 

5.362 
.360 

10.  724 
.720 

16.085 
.078 

21.448 
.439 

26.810 
.799 

Latitude 
interval. 

Meridi- 
onal 
distance. 

25 

.358 

.715 

.072 

.430 

.789 

30 

.354 

.708 

.060 

.415 

.768 

/ 

Inches. 

1 

6.060 

35 
371 

5.349 
.347 

10.698 
.694 

16.048 
.041 

21.  398 

.388 

26.  746 
.735 

2 
3 

12.120 
18.  178 

f)A      fWJQ 

40 
45 

.345 
.341 

.690 
.682 

.035 
.022 

.380 
.362 

.725 
.703 

4 
5 

24.  zoo 
30.  298 

50 

5.336 

10.673 

16.010 

21.348 

26.683 

521 
55 

.334 
.332 

.668 
.665 

.004 
15.  998 

.339 
.330 

.672 
.662 

Longi- 
tude 

Inch. 

60 

.328 

.657 

.985 

.312 

.640 

interval. 

29    00 

5.328 

10.657 

15.985 

21.312 

26.640 

1 

.000 

05 

.324 

.648 

.971 

.295 

.619 

2 

.002 

071 

.322 

.643 

.965 

.287 

.608 

3 

.003 

10 

.320 

.640 

.958 

.278 

.598 

4 

.006 

15 

.315 

.630 

.945 

.260 

.575 

5 

.010 

20 
221 
25 

5.310 
.308 
.306 

10.  621 
.617 
.612 

15.932 
.925 
.920 

21.  242 
.234 
.225 

26.553 
.542 
.532 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.302 

.605 

.907 

.209 

.511 

/ 

Inches. 

1 

6.060 

35 
371 
40 
45 

5.298 
.295 
.294 
.289 

10.596 
.591 
.587 
.578 

15.894 
.886 
.880 
.867 

21.  192 
.183 
.174 
.156 

26.490 
.478 
.468 
.445 

2 
3 
4 
5 

12.  121 
18.  182 
24.242 
30.302 

50 

5.284 

10.569 

15.853 

21.  137 

26.422 

521 

.282 

.565 

.847 

.130 

.412 

Longi- 

55 

.280 

.560 

.841 

.121 

.401 

tude 

Inch. 

60 

.275* 

.552 

.828 

.104 

.380 

interval. 

30    00 

5.275 

10.552 

15.828 

21.  104 

26.  380 

1 

.000 

05 

.272 

.543 

.815 

.086 

.358 

2 

.002 

071 

.269 

.538 

.808 

.077 

.346 

3 

.003 

10 

.267 

.534 

.801 

.068 

.335 

4 

.006 

15 

.262 

.525 

.787 

.050 

.312 

5 

.010 

20 
221 
25 

5.258 
.256 
.254 

10.516 
.512 
.507 

15.  774 
.768 
.760 

21.032 
.024 
.014 

26.290 
.280 
.268 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.249 

.499 

.748 

20.998 

.247 

f 

Inches. 

I 

6.061 

35 
371 

6.245 
.243 

10.490 
.485 

15.  735 

.728 

20.980 
.971 

26.225 
.213 

2 
3 

12.  122 

18.183 

40 

.240 

.480 

.721 

.961 

.202 

4     • 

24.  245 

45 

.236 

.472 

.708 

.944 

.180 

5 

30.305 

50 

5.232 

10.463 

15.  695 

20.927 

26.159 

521 

.229 

.459 

.688 

.918 

.147 

55 

.227 

.454 

.681 

.908 

.135 

60 

.222 

.445 

.667 

.890 

.112 

88  GEOGRAPHIC    TABLES    AND   FORMULAS. 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  i^oo) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinatesof  devel- 
oped parallel. 

Longitude  interval. 

Longi- 

1'. 

2'. 

3'. 

4'. 

5'. 

tude 

Inch. 

interval. 

o     / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

f 

31    00 

5.  222 

10.  445 

15.  667 

20  890 

26.  112 

1 

.000 

05 

.218 

.435 

.654 

.872 

.089 

2 

.002 

07^ 

.216 

.432 

.647 

.863 

.079 

3 

.003 

10 

.213 

.426 

.640 

.853 

.066 

4 

.006 

15 

.209 

.417 

.626 

.834 

.043 

5 

.010 

20 
22i 
25 

5.204 
.202 
.200 

10.  408 
.404 
.400 

15.  613 
.605 

.598 

20.  817 
.807 
.798 

26.  021 
.009 
25.998 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.195 

.390 

.585 

.780 

.975 

t 

Inches. 

1 

6.062 

85 

40° 
45 

5.190 
.188 
.186 
.181 

10.381 
.376 
.372 
.362 

15.  571 
.565 
.557 
.544 

20.762 
.753 
.743 
.725 

25.  952 
.941 
.929 
.906 

2 
3 
4 
5 

12.  124 

18.  187 
24.249 
30.  311 

50 

55* 
60 

5.177 
.174 
.172 
.167 

10.353 
.348 
.344 
.334 

15.530 
.523 
.516 
.502 

20.706 
.697 
.688 
.669 

25.  883 
.871 
.860 
.836 

Longi- 
tude 
interval. 

Inch. 

32    00 

5.167 

10.334 

15.502 

20.  669 

25.  836 

1 

.000 

05 

.162 

.325 

.487 

.650 

.812 

2 

.002 

(yji 

.160 

.320 

.480 

.640 

.800 

3 

.003 

10 

.158 

.315 

.473 

.630 

.788 

4 

.007 

15 

.153 

.305 

.458 

.611 

.764 

5 

.010 

20 
25* 

5.148 
.146 
.143 

10.296 
.291 
.286 

15.444 
.437 
.430 

20.  592 
.582 
.573 

25.740 
.728 
.716 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.139 

.277 

.416 

.554 

.693 

f 

Inches. 

1 

6.063 

35 

5.134 
.131 

10.268 
.263 

15.  401 
.394 

20.  535 
.526 

25.  669 
.659 

2 
3 

12.127 
18.190 

40* 
45 

.129 
.124 

.258 
.249 

.387 
.373 

.516 

.498 

.645 
.622 

4 
5 

24.254 
30.317 

5°i 

5.120 

10.  239 

15.  359 

20.478 

25.598 

55* 

.117 
.115 

.234 
.229 

.352 
.344 

.469 
.459 

.586 
.574 

Longi- 
tude 

Inch. 

60 

.110 

.220 

.330 

.440 

.550 

interval. 

33    00 

5.110 

10.220 

15.330 

20.  440 

25.550 

1 

.000 

05 

.105 

.210 

.316 

.421 

.526 

2 

.002 

07-1- 

.103 

.206 

.308 

.411 

.514 

3 

.003 

10 

.100 

.201 

.301 

.402 

.502 

4 

.007 

15 

.096 

.191 

.287 

.382 

.478 

5 

.010 

2°i 

5.091 
.088 

10.  182 
.176 

15.  272 
.264 

20.  363 
.352 

25.454 
.440 

Latitude 
interval. 

Meridi- 
onal 
distance. 

25* 

.086 

.171 

.257 

.342 

.428 

30 

.081 

.162 

.242 

.323 

.404 

j 

Inches. 

1 

6.065 

35 

40* 
45 

5.076 
.074 
*     .071 
.066 

10.  152 
.147 
.143 
.132 

15.228 
.220 
.213 
.199 

20.  304 
.294 
.285 
.265 

25.380 
.368 
.356 
.331 

2 
3 
4 
5 

12.  129 
18.  193 
24.258 
30.322 

50 

5.061 

10.  123 

15.184 

20.246 

25.307 

52i 

.059 

.118 

.177 

.236 

.295 

55 

.056 

.113 

.169 

.226 

.282 

60 

.052 

.103 

.156 

.     .206 

.258 

GEOGRAPHIC    TABLES    AND    FORMULAS.  89 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  Tuihro) — Continued. 


Abscissas  of  developed  parallel. 

Ordinates  of  devel- 

Latitude 
of 

Longitude  interval. 

oped  parallel. 

parallel. 

Longi- 

1'. 

2'. 

3'. 

4'. 

5'. 

tude 

Inch. 

. 

interval. 

o     / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

t 

34    00 

5.052 

10.103 

15.155 

20.206 

25.258 

1 

.000 

05 

.047 

.093 

.140 

.186 

.233 

2 

.002 

07i 

.044 

.089 

.132 

.176 

.220 

3 

.003 

10 

.042 

.083 

.125 

.166 

.208 

4 

.007 

15 

.037 

.073 

.110 

.146 

.183 

5 

.010 

20 
22* 
25 

5.032 
.029 
.027 

10.063 
.058 
.053 

15.095 
.087 
.080 

20.126 
.116 
.106 

25.158 
.145 
.133 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.022 

.043 

.065 

.086 

.108 

/ 

Inches. 

1 

6.065 

35 

g* 

5.017 
.014 
.012 

10.033 
.028 
.023 

15.050 
.042 
.035 

20.066 
.056 
.046 

25.083 
.070 
.058 

2 
3 
4 

12.  130 
18.  198 
24.  262 

45 

.007 

.013 

.020 

.026 

.033 

5 

30.  328 

50 

5.002 

10.003 

15.005 

20.006 

'   25.008 

52i 
55 
60 

4.999 
.997 
.992 

9.998 
.993 
.983 

14.997 
.990 
.976 

19.996 
.986 
.966 

24.  995 
.983 
.958 

Longi- 
tude 
interval. 

Inch. 

35    00 

4.992 

9.983  • 

14.  975 

19.966 

24.958 

1 

.000 

05 

.987 

.973 

.960 

.947 

.933 

2 

.002 

07* 

.984 

.968 

.952 

.936 

.920 

3 

-     .003 

10 

.982 

.963 

.945 

.926 

.908 

4 

.007 

15 

.976 

.953 

.929 

.906 

.882 

5 

.010 

20 

4.971 
.969 

9.942 
.937 

14.  913 
.906 

19.885 
.874 

24.856 
.843 

Latitude 
interval. 

Meridi- 
onal 
distance. 

25* 

.966 

.932 

.898 

.864 

.830 

30 

.961 

.922 

.883 

.844 

.805 

/ 

Inches. 

1 

6.067 

35 

4.956 

9.912 

14.868 

19.  824 

24.  780 

2 
3 

12.  133 
18.  200 

37i 
40 

45 

.953 
.951 
.946 

.907 
.902 
.891 

.860 
.853 
.837 

.814 
.805 
.783 

.767 
.754 
.728 

4 

5 

24!  266 
30.333 

*    50 

4.940 

9.881 

14.  821 

19.  762 

24.  702 

65* 
60 

.938 
.935 
.930 

.876 
.871 
.861 

.814 
.806 
.791 

.752 
.742 
.722 

.690 
.677 
.652 

Longi- 
tude 
interval. 

Inch. 

36    00 

4.930 

9.861 

14.  791 

19.  722 

24.  652 

'  1 

.000 

05 

.925 

.850 

.776 

.701 

.626 

2 

.002 

.923 

.845 

.768 

.690 

.613 

3 

.005 

10 

.920 

.840 

.760 

.680 

.600 

4 

.007 

15 

.915 

.830 

.745 

.660 

.574 

5 

.010 

20 
22i 

4.910 
.907 

9.819 
.814 

14.  719 
.721 

19.  638 
.628 

24.548 
.535 

Latitude 
interval. 

Meridi- 
onal 
distance. 

26 

.904 

.808 

.712 

.617 

.521 

30 

.899 

.798 

.697 

.596 

.495 

/ 

Inches. 

1 

6.067 

35 
37i 
40 

4.894 
.891 

.888 

9.787 

.782 
.777 

14.681 
.673 
.665 

19.  574 
.664 
.554 

24.  468 
.465 
.442 

2 
3 
4 

K    " 

12.  135 
18.  202 
24.  269 

on   qqfi 

45 

.883 

.766 

.649 

.532 

.415 

0 

oU.  OOO 

50 

4.878 

9".  756 

14.633 

19.  512 

24.389 

52| 

.875 

.750 

.626 

.501 

.376 

55 

.873 

.745 

.618 

.490 

.363 

60 

.868 

.735 

.603 

.470 

.338 

90  GEOGRAPHIC   TABLES    AND    FORMULAS. 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  j^y^) — Continued. 


Abscissas  of  developed  parallel. 

Ordinates  of  devel- 

Latitude 
of 

oped  parallel. 

Longitude  interval. 

parallel. 

r. 

2'. 

3'. 

4'. 

5'. 

Longi- 
tude 

Inch. 

interval. 

o     / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

, 

37    00 

4.868 

9.735 

14.603 

19.  470 

24.338 

1 

.000 

06 

.862 

.724 

.586 

;448 

.310 

2 

.002 

.859 

.718 

.578 

.437 

.296 

3 

.005 

10* 

.856 

.713 

.569 

.426 

.282 

4 

.007 

15 

.851 

.702 

.553 

.404 

.255 

5 

.010 

20 

4.846 
.843 

9.691 

.686 

14.537 
.529 

19.382 
.372 

24.  228 
.215 

Latitude 
interval. 

Meridi- 
onal 
distance. 

25S 

.840 

.680 

.521 

.362 

.202 

30 

.835 

.670 

.505 

.340 

.175 

/ 

Inches. 

1 

6.068 

35 
37i 
40 

4.830 

.827 
.824 

9.659 
.654 
.649 

14.  489 
.481 
.473 

19.  318 
.308 
.298 

24.  148 
.135 
.122 

2 
3 
4 

12.  136 
18.  205 
24.  273 

45 

.819 

.638 

.457 

.276 

.095 

50 

4.814 

9.627  ' 

14.441 

19.254 

24.068 

55 
60 

.811 
.808 
.802 

.622 
.616 
.605 

.432 
.424 
.407 

.243 
.232 
.209 

.054 
.040 
.012 

Longi- 
tude 
interval. 

Inch. 

38    00 

4.802 

9.605 

14.  407 

19.  209 

24.  012 

1 

.000 

05 

.797 

.594 

.391 

.188 

23.  985 

2 

.002 

07* 

.794 

.589 

.383 

.178 

.972 

3 

.005 

10 

.792 

.584 

.375 

.167 

.959 

4 

.007 

15 

.786 

.673 

.359 

.146 

.932 

5 

.010 

20 

4.781 

.778 

9.562 
.556 

14.  343 
.335 

19.  124 
.113 

23.905 
.891 

Latitude 
interval. 

Meridi- 
onal dis- 
tance. 

25" 

.776 

.551 

.326 

.102 

.878 

30 

.770 

.640 

.310 

.080 

.850 

t 

Inches. 

1 

6.069 

35 

40* 
45 

4.764 
.762 
.759 
.754 

9.529 
.524 
.518 
.507 

14.  293 
.286 

.277 
.261 

19.058 
.047 
.036 
.015 

23.  822 
.809 
.795 
.768 

2 
3 
4 
5 

12.138 
18.  207 
24.  277 
30.  345 

50 

4.748 

9.496 

14.  244 

18.  993 

23.740 

52* 
55 
60 

.745 
.742 
.737 

.490 
.485 
.474 

,236 
.227 
.211 

.981 
.970 
.948 

.726 
.712 
.685 

Longi- 
tude 
interval. 

Inch. 

39    00 

4.737 

9.474 

14.211 

18.948 

23.685 

1 

.000 

05 

.731 

.463 

.194 

.926 

.657 

2 

.002 

07i 

.728 

.457 

.185 

.914 

.642 

3 

.005 

10 

.726 

.451 

.177 

.902 

.628 

4 

.007 

15 

.720 

.440 

.160 

.880 

.600 

5 

.010 

20  1 

4.714  ' 
.712 

9.429 
.423 

14.  143 
.135 

18.  858 
.846 

23.  572 
.558 

Latitude 
interval. 

Meridi- 
onal 
distance. 

25* 

.709 

.417 

.126 

.835 

.544 

30 

.703 

.407 

.119 

.813 

.516 

/ 

Inches. 

1 

6.070 

35 
37i 
40 
45 

4.698 
.695 
.692 
.686 

9.395 
.389 
.384 
.373 

14.093 
.084 
.076 
.059 

18.790 
.779 
.768 
.746 

23.488 
.474 
.460 
.432 

2 
3 
4 
5 

12.  140 
18.  210 
24.281 
30.351 

50j 

4.681 

9.362 

14.042 

18.  723 

23.404 

.678 

.356 

.034 

.712 

.390 

55S 

.675 

.350 

.025 

.700 

.375 

60 

.669 

.339 

.008 

.678 

.347 

GEOGRAPHIC   TABLES    AND   FORMULAS.  91 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  TSTT^) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

If. 

2'. 

3'. 

4'. 

5'. 

Longi- 
tude 
interval. 

Inch. 

o     / 
40    00 
05 
07i 
10 
15 

20 
22i 
25 
30 

35 
37i 
40 
45 

50 
52* 
55 
60 

41    00 
05 
07| 
10 
15 

20 
22i 
25 
30 

35 
3?£ 
40 
45 

50 
52£ 
55 

42    00 
05 
07* 
10 
15 

20 
22£ 
25 
30 

35 
37i 
40 
45 

50 
52J 
55 
60 

Inches. 
4.669 
.664 
.661 
.658 
.652 

4.647 
.644 
.641 
.635 

4.630 
.627 
.624 
.618 

4.612 
.609 
.606 
.600 

4.600 
.595 
.592 
.589 
.583 

4.577 
.574 
.571 
.566 

4.560 
.557 
.554 

.548 

4.542 
.539 
.536 

4.530 
.524 
.521 
.518 
.513 

4.507 
.504 
.501 
.495 

4.489 
.486 
.483 
.477 

4.471 
.468 
.465 
.459 

Inches. 
9.339 
.328 
.322 
.316 
.305 

9.293 
.288 
.282 
.271 

9.259 
.253 
.248 
.236 

9.224 
.219 
.213 
.201 

9.201 
.189 
.183 
.178 
.166 

9.154 
.149 
.143 
.131 

9.119 
.114 
.108 
.0% 

9.084. 
.078 
.072 

9.060 
.049 
.043 
.037 
.025 

9.013 
.007 
.002 
.990 

8.978 
.972 
.966 
.954 

8.942 
.936 
.930 
.918 

Inches. 
14.008 
13.  991 
.983 
.975 
.957 

.  13.940 
.931 
.923 
.906 

13.889 
.880 
.871 
.854 

13.837 
.828 
.819 
.801 

13.801 
.784 
.775 
.766 
.749 

13  732 
.723 
.714 
.697 

13.  679 
,670 
,661 
.644 

13.  626 
.617 
.608 

13.  591 
.572 
,564 
.555 
.537 

13.  520 
.511 

.502 

.484 

13.  467 
.458 
.449 
.431 

13.413 
.404 
.395 
.377 

Inches. 
18.  678 
.655 
.644 
.632 
.610 

18.586 
.575 
.564 
.542 

18.  518 
.507 
.495 
.472 

18.449 
.438 
.426 
.402 

18.402 
.378 
.368 
.355 
.332 

18.309 
.298 
.286 
,262 

18.  239 
.227 
.215 
.192 

18.168 
.156 
.145 

18.  122 
.098 
.086 
.073 
.050 

18.  027 
.014 
.003 
17.  979 

17.956 
.944 
.932 
.908 

17.884 
.872 
.860 
.836 

Inches, 
23.  347 
.319 
.305 
.291 
.262 

23.233 
.219 
.205 
.177 

23.  148 
.134 
.119 
.090 

23.061 
.047 
.032 
.002 

23.002 
22.973 
.958 
.944 
.915 

22.886 
.872 
.857 
.828 

22.798 
.784 
.769 
.740 

22.710 
.695 
.681 

22.652 
.622 
.607 
.592 
.563 

22.533 
.518 
.504 
.474 

22.445 
.430 
.415 
.385 

22.355 
.340 
.325 
.295 

1 
2 
3 
4 
5 

.000 
.002 
,005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

1 

2 
3 

4 
5 

Inches. 
6.072 
12.  143 
18.215 
24.  286 
30.358 

Longi- 
tude 
interval. 

Inch. 

t 
1 
2 
3 
4 
5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

/ 
1 
2 
3 
4 
5 

Inches. 
6.072 
12.  145 
18.  218 
24.290 
30.  362 

Longi- 
tude 
interval. 

Inch. 

t 

1 
2 
3 
4 
5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

1 

2 
3 
4 
5 

Inches. 
6.073 
12.  148 
18.220 
24.294 
30.367 

92  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  10. — Coordinates  for  the.  projection  of  maps  (scale  y^iy^oO — Continued 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

1'. 

2'. 

3'. 

4'. 

5'. 

Longi- 
tude 
interval. 

Inch. 

0       / 

43    00 
05 
07£ 
10 
15 

20 
22£ 
25 
30 

35 
37| 
40 
45 

50 
52i 
55 
60 

44    00 
05 
07| 
10 
15 

20 
22i 
25 
30 

35 
37i 
40 
45 

50 
52i 
55 
60 

45    00 
05 
07* 
10 

15 

20 
22i 
25 
30 

35 
37i 
40 
45 

50 
62| 

55 
60 

Inches. 
4.459 
.453 
.450 
.447 
.441 

4.434 
.431 
.428 
.422 

4.416 
.413 
.410 
.404 

4.398 
.395 
.392 
.386 

4.386 
.380 
.376 
.373 
.367 

4.361 
.358 
,355 
.349 

4.342 
.339 
.336 
.330 

4.324 
.321 
.318 
.312 

4.312 
.305 
.302 
.299 
.293 

4.287 
.283 
.280 
.274 

4.268 
.264 
.261 
.255 

4.249 
.246 
.242 
.236 

Inches. 
8.918 
.906 
.899 
.894 
.882 

8.869 
.863 
.856 
.844 

8.832 
.826 
.820 
1808 

8.796 
.789 
.784 
.772 

8.772 
.759 
.753 
.747 
.734 

8.722 
.716 
.709 
.697 

8.685 
.678 
.672 
.660 

8.648 
.642 
.635 
.623 

8.623 
.610 
.604 
.598 
.586 

8.573 
.567 
.560 

.548 

8.535 
.529 
.522 
.510 

8.497 
.491 
.485 
.472 

Inches. 
13.377 
.359 
.349 
.340 
.322 

13.303 
.294 
.285 
.266 

13.248 
.239 
.230 
.212 

13.  194 
.184" 
.175 
.157 

13.  157 
.139 
.129 
.120 
.102 

13.  083 
.074 
.064 
.046 

13.  027 
.018 
.009 
12.990 

12.971 
.963 
.953 
.935 

12.935 
.916 
.906 
.897 
.878 

12.  860 
.849 
.841 
.822 

12.  803 
.793 
.784 
.765 

12.746 
.737 
.727 
.707 

Inches. 
17.836 
.812 
.799 
.787 
.762 

17.738 
.726 
.713 
.688 

17.664 
.652 
.640 
.616 

17.  592 
.579 
.567 
.543 

17.543 
.518 
.506 
.494 
.469 

17.  444 
.431 
.419 
.394 

17.  370 
.357 
.345 
.320 

17.  295 
.283 
.270 
.246 

17.246 
.221 
.208 
.196 
.171 

17.146 
.134 
.121 
.096 

17.070 
.058 
.045 
.020 

16.995 
.982 
.970 
.944 

Inches'. 
22.295 
.265 
.249 
.234 
.203 

22.  172 
.157 
.141 
.110 

22.  080 
.065 
.050 
.020 

21.990 
.974 
.959 
.929 

21.  929 

.898 
.882 
.867 
.836 

21.805 
.789 
.774 
.743 

21.  712 
.696 
.681 
.650 

•21.619 
.604 
.588 
.558 

21.558 
.527 
.511 
.495 
.464 

21.433 
.417 
.401 
.370 

21.  338 
.322 
.306 
.275 

21.243 
.228 
.212 
.180 

r 

I 
2 
3 
4 

5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

f 
1 
2 
3 
4 
5 

Inches. 
6.075 
12.  149 
18.  223 
24.298 
30.  372 

Longi- 
tude 
interval. 

Inch. 

/ 
1 
2 
3 
4 
5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

/ 
1 
2 
3 

4 
5 

Inches. 
6.076 
12.  152 
18.228 
24.304 
30.380 

Longi- 
tude 
interval. 

Inch: 

t 
1 
2 
3 
4 
5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

/ 
1 
2 
3 
4 
5 

Inches. 
6.077 
12.154 
18.231 
24.308 
30.385 

GEOGRAPHIC  TABLES  AND  FORMULAS.  93 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  ystUff) — Continued. 


Latitude 
of 
parallel. 

Abscissas  of  developed  parallel. 

Ordinates  of  devel- 
oped parallel. 

Longitude  interval. 

1'. 

2'. 

3'. 

4'. 

5'. 

Longi- 
tude 
interval. 

Inch. 

O      ' 

46    00 
05 
07i 
10 
15 

20 
22* 
25 
30 

35 
37i 
40 
45 

50 
52* 
55 
60 

47    00 
05 
07* 
10 
15 

20 
22* 
25 
30 

35 

S1 

45 

50 
52* 
55 
60 

48    00 
05 
07* 
10 
15 

20 
224 
25 
30 

35 
37* 
40 
45 

50 
52i 
55 
60 

Inches. 
4.236 
.229 
.226 
.223 
.216 

4.210 
.207 
.204 
.198 

4.191 

.188 
.184 
.178 

4.172 
.168 
.165 
.159 

4.159 
.152 
.149 
.146 
.139 

4.133 
.130 
.126 
.120 

4.113 
.110 
.106 
.100 

4.094 
.090 
.089 
.080 

4.080 
.074 
.071 
.067 
.061 

4.054 
.051 
.048 
.041 

4.034 
.031 
.028 
.021 

4.014 
.011 

.008 
.001 

Inches. 
8.472 
.459 
.452 
.446 
.433 

8.420 
.414 
.408 
.395 

8.382 
.376 
.369 
.356 

8.343 
.337 
.330 
.318 

8.318 
.305 
.299 
.292 
.279 

8.266 
.259 
.252 
.239 

8.226 
.220 
.213 
.200 

8.187 
.180 
.174 
.161 

8.160 
.148 
.142 
.135 
.     .  122 

8.108 
.102 
.095 
.082 

8.069 
.062 
.055 
.042 

8.029 
.022 
.016 
.002 

Inches. 
12.  707 
.688 
.679 
.669 
.649 

12.630 
.621 
.611 
.593 

12.573 

.564 
.553 
.534 

12.  515 
.505 
.4% 
.476 

12.  476 
.457 
.448 
.438 
.418 

12.  398 
.389 
.378 
.359 

12.339 
.329 
.319 
.300 

12.281 
.271 
.261 
.241 

12.241 
.222 
.212 
.202 

.182 

12.  162 
.153 
.143 
.123 

12.  103 
.093 
.083 
.063 

12.043 
.034 
.024 
.003 

Inches. 
16.944 
.918 
.905 
.892 
.867 

16.840 
.828 
.815 
.790 

16.764 
.752 
.738 
.712 

16.687 
.674 
.661 
.635 

16.635 
.610 
.597 

.584 
.558 

16.531 
.518 
.505 
.478 

16.  452 
.439 
-.426 
.400 

16.  375 
.361 
.348 
.322 

16.321 
.296 
.284 
.270 
.244 

16.217 
.204 
.190 
.164 

16.  138 
.124 
.110 

.084 

16.  058 
.045 
.031 
.004 

Inches. 
21.  179 
.147 
.131 
.115 
.082 

21.051 
.035 
.019 
20.988 

20.955 
.939 
.922 
.890 

20.858 
.842 
.826 
.794 

20.  794 
.762 
.746 
.730 
.697 

20.664 
.648 
.631 
.598 

20.565 
.549 
.532 
.500 

20.468 
.451 
.435 
.402 

20.  401 
.370 
.354 
.337 
.304 

20.  271 
.255 
.238 
.205 

20.  172 
.155 
.138 
.105 

20.  072 
.056 
.039 
.006 

1 
2 

3 
4 

5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

1 
2 
3 
4 
5 

Inches. 
6.078 
12.  157 
18.  235 
24.  313 
30.391 

^ 

Longi- 
tude 
interval. 

Inch. 

1 
2 
3 
4 
5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

1 
2 
3 
4 
5 

Inches. 
6.078 
12.  157 
18.  235 
24.  315 
30.392 

Longi- 
tude 
interval. 

Inch. 

1 
2 
3 
4 
5 

.000 
.002 
.005 
.007 
.010 

Latitude 
interval. 

Meridi- 
onal 
distance. 

1 

2 
3 
4 
5 

Inches. 
6.080 
12.160 
18.  240 
24.  320 
30.400 

94  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  10. — Coordinates  for  the  projection  of  maps  (scale  T^O) — Continued. 


Abscissas  of  developed  parallel. 

Ordinates  of  devel- 

Latitude 
of 

Longitude  interval. 

oped  parallel. 

parallel. 

Longi- 

1'. 

2'. 

3'. 

4'. 

5'. 

tude 

Inch. 

interval. 

0       / 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

, 

49    00 

4.001 

8.002 

12.  003 

16.004 

20.006 

1 

.000 

05 

3.995 

7.989 

11.  984 

15.  978 

19.  973 

2 

.002 

07| 

.991 

.982 

.974 

.965 

.956 

3 

.005 

10 

.988 

.976 

.964 

.952 

.939 

4 

.007 

15 

.981 

.962 

.943 

.924 

.905 

5 

.010 

20 
22i 
25 

3.974 
.971 
.968 

7.949 
.942 
.936 

11.923 
.914 
.904 

15.  898 
.885 
.872 

19.  872 
.856 
.840 

Latitude 
interval. 

Meridi- 
onal 
distance. 

30 

.961 

.922 

.883 

.844 

.805 

' 

Inches. 

\ 

6.081 

35 

3.954 

7.908 

11.863 

15.817 

19.  771 

2 

12  162 

37i 
40 
45 

.951 
.948 
.941 

• 

.902 
.895 
.882 

.853 
.843 
.823 

.804 
.790 
.764 

.755 
.738 
.705 

3 
4 
5 

18!  243 
24.  324 
30.405 

50 

3.934 

7.869 

11.803 

15.738 

19.  672 

52i 

.931 

.862 

.793 

.724 

.655 

55 

.928 

.855 

.783 

.710 

.638 

60 

.921 

.842 

.762 

.683 

.604 

GEOGRAPHIC    TABLES    AND    FOEMULAS. 


95 


TABLE  11. — Areas  of  quadrilaterals  of  earth's  surface  of  1°  extent  in  latitude  and 

longitude. 

From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

0     / 

o   / 

0     / 

0  00 
0  30 
1  00 
1  30 

4,  752.  33 
4,  752.  16 
4,  751.  63 
4,  750.  75 

22  00 
22  30 
23  00 
23  30 

4,  414.  67 
4,  399.  30 
4,  383.  60 
4,  367.  57 

44  00 
44  30 
45  00 
45  30 

3,440.98 
3,  412.  26 
3,  383.  27 
3,354.01 

2  00 
2  30 
3  00 
3  30 

4,  749.  52 
4,747.93 
4,746.00 
4,  743.  71 

24  00 
24  30 
25  00 
25  30 

4,  351.  21 
4,  334.  52 
4,  317.  51 
4,  300.  17 

46  00 
46  30 
47  00 
47  30 

3,  324.  49 
3,  294.  71 
3,264.68 
3,  234.  39 

4  00 
4  30 
5  00 
5  30 

4,  741.  07 
4,738.08 
4,  734.  74 
4,731.04 

26  00 
26  30 

27  00 
27  30 

4,  282.  50 
4,  264.  51 
4,  246.  20 
4,  227.  56 

48  00 
48  30 
49  00 
49  30 

3,  203.  84 
3,  173.  04 
3,141.99 
3,  110.  69 

6  00 

6  30 
7  00 
7  30 

4,  727.  00 
4,  722.  61 
4,  717.  86 
4,  712.  76 

28  00 
28  30 
29  00 
29  30 

4,  208.  61 
4,  189.  33 
4,  169.  74 
4,  149.  83 

50  00 
50  30 
51  00 
51  30 

3,  079.  15 
3,047.37 
3,  015.  34 
2,  983.  08 

8  00 
8  30 
9  00 
9  30 

4,  707.  32 
4,  701.  52 
4,  695.  38 
4,  688.  89 

30  00 
30  30 
31  00 
31  30 

4,  129.  60 
4,  109.  06 
4,  088.  21 
4,  067.  05 

52  00 
52  30 
53  00 
53  30 

2,  950.  58 
2,  917.  85 
2,  884.  88 
2,  851.  68 

10  00 
10  30 
11  00 
11  30 

4,  682.  05 
4,  674.  86 
4,  667.  32 
4,  659.  43 

32  00 
32  30 
33  00 
33  30 

4,  045.  57 
4,  023.  79 
4,  001.  69 
3,  979.  30 

54  00 
54  30 
55  00 
55  30 

2,  818.  27 
2,  784.  62 
2,  750.  76 
2,  716.  67 

12  00 
12  30 
13  00 
13  30 

4,  651.  20 
4,  642.  63 
4,  633.  71 
4,624.44 

34  00 
34  30 
35  00 
35  30 

3,  956.  59 
3,  933.  59 
3,  910.  28 
3,  886.  67 

56  00 
56  30 

57  00 
57  30 

2.682.37 
2,  647.  85 
2,  613.  13 

2,  578.  19 

14  00 
14  30 
15  00 
15  30 

4,  614.  82 
4,  604.  87 
4,  594.  57 
4,583.92 

36  00 
36  30 
37  00 
37  30 

3,  862.  76 
3,  838.  56 
3,814.06 
3,  789.  26 

58  00 
58  30 
59  00 
59  30 

2,  543.  05 
2,  507.  70 
2,  472.  16 
2,  436.  42 

16  00 
16  30 
17  00 
17  30 

4,  572.  94 
4,  561.  61 
4,  549.  94 
4,  537.  93 

38  00 
38  30 
39  00 
39  30 

3,  764.  18 
3,  738.  80 
3,  713.  14 
3,  687.  18 

60  00 
60  30 
61  00 
61  30 

2,  400.  48 
2,  364.  34 
2,328.02 
2,  291.  51 

18  00 
18  30 
19  00 
19  30 

4,  525.  59 
4,  512.  90 
4,  499.  87 
4,  486.  51 

40  00 
40  30 
41  00 
41  30 

3,  660.  95 
3,  634.  42 
3,  607.  62 
3,  580.  54 

62  00 
62  30 
63  00 
63  30 

2,  254.  82 
2,  217.  94 
2,  180.  89 
2,  143.  66 

20  00 
20  30 
21  00 
21  30 

4,472.81 
4,  458.  78 
4,  444.  41 
4,429.71 

42  00 
42  30 
43  00 
43  30 

3,  553.  17 
3,  525.  54 
3,  497.  62 
3,  469.  44 

64  00 
64  30 
65  00 
65  30 

2,  106.  26 
2,  068.  68 
2,  030.  94 
1,  993.  04 

96 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  11. — Areas  of  quadrilaterals  of  earth's  surface  of  1°  extent  in  latitude  and 

longitude — Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

o        / 

0            / 

o       / 

66    00 
66    30 
67     00 
67     30 

1,  954.  97 
1,  916.  75 
1,  878.  37 
1,  839.  84 

76     00 
76     30 

77     00 
77     30 

1,  164.  49 
1,  123.  75 
1,  082.  91 
1,  041.  99 

86    00 
86    30 
87    00 
87    30 

336.  02 
294.08 
252.  11 
210.  12 

68    00 
68    30 
69    00 
69     30 

1,  801.  16 
1,762.33 
1,  723.  36 
1,  684.  24 

78    00 
78     30 
79    00 
79     30 

1,  000.  99 
959.90 
918.  73 
877.49 

88    00 
88    30 
89    00 
89    30 

168.  12 
126.  10 
84.07 
42.04 

70    00 
70    30 
71    00  ' 
71    30 

1,  645.  00 
1,  605.  62 
1,  566.  10 
1,526.46 

80    00 
80    30 
81    00 
81     30 

836.  18 
794.  79 
753.  34 
711.83 

90    00 

00.00 

72    00 
72    30 
73    00 
73    30 

1,  486.  70 
1,  446.  81 
1,  406.  81 
1,  366.  69 

82    00 
82    30 
83    00 
83    30 

670.  27 
628.  64 
586.  97 
545.  24 

74    00 
74    30 
75    00 

75    30 

1,326.46 
1,  286.  12 
1,  245.  68 
1,  205.  13 

84    00 
84    30 
85    00 
85    30 

503.  47 
461.  66 
419.  81 
377.93 

GEOGRAPHIC    TABLES    AND    FORMULAS, 


97 


TABLE  12. — Areas  of  quadrilaterals  of  earth's  surface  of  30f  extent  in  latitude  and 

longitude. 

[From  Smithsonian  Geographical  Tables.  | 


Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

0           / 

o       / 

0           / 

0    00 
0    15 
0    30 
0    45 

1,  188.  10 
1,188.08 
1,  188.  05 
1,188.00 

11     00 
11     15 
11     30 
11    45 

1,  166.  84 
1,  165.  86 
1,  164.  86 
1,  163.  85 

22    00 
22    15 
22    30 
22    45 

1,  103.  68 
1,  101.  77 
1,  099.  84 
1,097.88 

1    00 
1     15 
1    30 
1    45 

1,187.92 
1,  187.  82 
1,  187.  70 
1J87.56 

12    00 
12    15 
12    30 
12    45 

1,  162.  81 
1,  161.  75 
1,  160.  67 
1,  159.  56 

23    00 
23    15 
23    30 
23    45 

1,  095.  91 
1,093.92 
1,091.90 
1,089.87 

2    00 
2    15 
2    30 

2    45 

1,  187.  39 
1,  187.  20 
1,  186.  99 
1,J86.76 

13    00 
13    15 
13    30    ! 
13    45 

,158.44 
,  157.  29 
,  156.  12 
,  154.  93 

24    00 
24    15 
24    30 
24    45 

1,  087.  81 
1,085.74 
1,  083.  64 
1,  081.  52 

3    00 
3    15 
3    30 
3    45 

1,  186.  51 
1,  186.  24 
1,  185.  95 
1,  185.  62 

14    00 
14    15 
14    30 
14    45 

,  153.  72 
,  152.  48 
,  151.  23 
,  149.  95 

25    00 
25    15 
25    30 
25    45 

1,  079.  39 
1,  077.  23 
1,  075.  05 
1,072.85 

4    00 
4    15 
4    30 
4    45 

1,  185.  28 
1,  184.  92 
,  184.  53 
,  184.  13 

15    00 
15    15 
15    30 
15    45 

,  148.  65 
,  147.  33 
,  145.  99 
,  144.  63 

26    00 
26    15 
26    30 

26    45 

1,  070.  64 
1,  068.  40 
1,  066.  14 
1,  063.  86 

5    00 
5    15 
5    30 
5    45 

,  183.  70 
,  183.  24 

,  182.  77 
,  182.  28 

16    00 
16    15 
16    30 
16    45 

,  143.  25 
,  141.  84 
,  140.  41 
,  138.  96 

27    00 
27    15 
27    30 
27    45 

1,  061.  56 
1,  059.  24 
1,  056.  90 
1,  054.  54 

6    00 
6    15 
6    30 
6    45 

1,  181.  76 
1,  181.  22 
1,  180.  66 
1,  180.  08 

17    00 
17    15 
17    30 
17    45 

,  137.  60 
,  136.  00 
1,104.49 
1,  132.  96 

28    00 
28    15 
28    30 
28    45 

1,  052.  16 
1,  049.  76 
1,047.34 
1,044.90 

7    00 
7    15 
7    30 
7    45 

1,  179.  48 
1,  178.  85 
1,  178.  20 
1,  177.  53 

18    00 
18    15 
18    30 
18    45 

1,131.41 
1,  129.  83 
1,  128.  24 
1,  126.  62 

29    00 
29    15 
29    30 
29    45 

1,  042.  44 
1,  039.  97 
1,  037.  47 
1,034.95 

8    00 
8    15 
8    30 
8    45 

1,  176.  84 
1,  176.  13 
1,  175.  39 
1,  174.  63 

19    00 
19    15 
19    30 
19    45 

1,  124.  98 
1,  123.  32 
1,121.64 
1,  119.  93 

30    00 
30    15 
30    30 
30    45 

1,  032.  41 
1,029.85 
1,027.27 
1,024.68 

9    00 
9    15 
9    30 
9    45 

1,  173.  86 
1,  173.  06 
1,  172.  23 
1,  171.  39 

20    00 
20    15 
20    30 
20    45 

1,118.21 
1,116.47 
1,  114.  71 
1,  112.  92 

31    00 
31    15 
31    30 
31    45 

1,022.06 
1,019.43 
1,016.77 
1,  014.  10 

10    00 
10    15 
10    30 
10    45 

1,170.52 
1,  169.  63 
1,  168.  73 
1,  167.  80 

21    00 
21    15 
21    30 
21    45 

1,  111.  11 
1,  109.  28 
1,107.44 
1,105.57 

32    00 
32    15 
32    30 
32    45 

1,011.40 
1,  008.  69 
1,  005.  96 
1,003.20 

40001  —  08 7 


98 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  12. — Areas  of  quadrilaterals  of  earth's  surface  of  30'  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 
square  miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in 

square  miles. 

o       / 

0            / 

0              / 

33     00 

1,000.43 

44    00 

860.  25 

55    00 

687.  70 

33     15 

997.64 

44     15 

856.  67 

55    15 

683.  44 

33    30 

994.  83 

44    30 

853.  07 

55    30 

679.  17 

33    45 

992.00 

44    45 

849.  46 

55    45 

674.  89 

34    00 

989.  16 

45    00 

845.  82 

56    00 

670.  60 

34    15 

986.  29 

45     15 

842.  18 

56    15 

666.  29 

34    30 

983.  41 

45     30 

838.  51 

56    30 

661.  97 

34    45 

980.  50 

45    45 

834.  83 

56    45 

657.  64 

35    00 

977.  58 

46    00 

831.  13 

57    00 

653.  29 

35    15 

974.64 

46     15 

827.  42 

57     15 

648.  93 

35    30 

971.  68 

46   .30 

823.  68 

57    30 

644.  55 

35    45 

968.  70 

46    45 

819.  94 

57    45 

640.  17 

36    00 

965.  70 

47    00 

816.  18 

58    00 

635.  77 

36    15 

962.  68 

47    15 

812.40 

58    15 

631.36 

36    30 

959.  65 

47    30 

808.  60 

58    30 

626.  93 

36    45 

956.  60  . 

47    45 

804.  79 

58    45 

622.  49 

37    00 

953.  52 

48    00 

800.  97 

59    00    !        618.05 

37     15 

950.  43 

48    15 

797.  13 

59    15     !        613.59 

37    30 

947.  32 

48    30 

793.  27 

59    30    j        609.11 

37    45 

944.21 

48    45 

789.  39 

59    45 

604.  62 

38    00 

941.  05 

49    00 

785.  50 

60    00 

600.  13 

38    15 

937.  88 

49    15 

781.  60 

60    15 

595.  62 

38    30 

934.  71 

49    30 

777.  68 

60    30 

591.  09 

38    45 

931.  51 

49    45 

773.  74 

60    45 

586.  56 

39    00 

928.  29 

50    00 

769.  79 

61    00 

582.  01 

39    15 

925.  06 

50    15 

765.  83 

61     15 

577.  45 

39    30 

921.  80 

50    30 

761.  85 

61     30    i        572.88 

39  .45 

918.  53 

50    45 

757.  85 

61    45    ;        568.30 

i 

I 

40    00 

915.  25 

51    00 

753.84 

62    00    i        563.71 

40    15 

911.  94 

51     15 

749.  82 

62    15 

559.  11 

40    30 

908.  61 

51     30 

745.  78 

62    30 

554.  49 

40    45 

905.  27 

51     45 

741.  72 

62    45 

549.  86 

41    00 

901.  91 

52    00 

737.  65 

63    00 

545.  23 

41     15 

898.  54 

52    15 

733.  57 

63    15 

540.  58 

41     30 

895.  14 

52    30 

729.  47 

63    30 

535.  92 

41    45 

891.  73 

52    45 

725.  36 

63    45 

531.  25 

42    00 

888.  30 

53    00 

721.  23 

64    00 

526.57 

42    15 

884.  85 

53    15 

717.  08 

64    15 

521.  88 

42    30 

881.  39 

53    30 

712.  93 

64    30 

517.  17 

42    45 

877.  91 

53    45 

708.  76 

64    45 

512.  46 

43    00 

874.  41 

54    00 

704.  57 

65    00 

507.  74 

43    15 

870.  90 

54    15 

700.  38 

65    15 

503.  01 

43    30 

867.  37 

54    30 

696.  16 

65    30 

498.  26 

43    45 

863.  82 

54    45 

691.  94 

65    45 

493.  51 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


99 


TABLE  12.—  Areas  of  quadrilaterals  of  earth's  surface  of  SO'  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilat- 
eral. 

Area  in  square 
miles. 

Middle  latitude 
of  quadrilat- 
eral. 

Area  in  square 
miles. 

Middle  latitude 
of  quadrilat- 
eral. 

Area  in  square 
miles. 

0             / 

66    00 
66    15 
66    30 
66    45 

488.  75 
483.  97 
479.  19 
474.  40 

0             / 

74    00 
74    15 
74    30 
74    45 

331.  62 
326.  58 
321.  53 
316.  48 

0             / 

82    00 
82    15 
82    30 
82    45 

167.  57 
162.  37 
157.  16 
151.  95 

67    00 
67    15 
67    30 
67  '45 

469.  60 
464.78 
459.  96 
455.  13 

75    00 
75    15 
*75    30 
75    45 

311.  42 
306.  36 
301.  28 
296.  21 

83    00 
83    15 
83    30 
83    45 

146.  74 
141.  53 
136.  31 
131.  09 

68    00 
68    15 
68    30 
68    45 

450.  29 
445.45 
440.  59 
435.72 

76    00 
76    15 
76    30 
76    45 

291.  12 
286.04 
280.  94 
275.84 

84    00 
84    15 
84    30 
84    45 

125.  87 
120.64 
115.  42 
110.  18 

69    00 
69    15 
69    30 
69    45 

430.  84 
425.  96 
421.06 
416.  16 

77    00 
77    15 
77    30 
77    45 

270.  73 
265.62 
260.  50 
255.  38 

85    00 
85    15 
85    30 
85    45 

104.95 
99.72 
94.48 
89.25 

70    00 
70    15 
70    30 
70    45 

411.  25 
406.34 
401.  41 
396.  47 

78    00 
78    15 
78    30 
78    45 

250.  25 
245.  12 
239.  98 
234.  83 

86    00 
86    15 
86    30 
86    45 

84.01 
78.76 
73.52 
68.27 

71    00 
71     15 
71    30 
71    45 

391.  53 
386.58 
381.62 
376.65 

79    00 
79    15 
79    30 

79    45 

229.68 
224.  53 
219.  37 
214.  21 

87    00 
87    15 
87    30 
87    45 

63.03 
57.  78 
52.53 
47.28 

72    00 
72    15 
72    30 

72    45 

371.  68 
366.70 
361.  71 
356.  71 

80    00 

80    15 
80    30 
80.  45 

209.  05 
203.  88 
198.  70 
193.  52 

88    00 
88    15 
88    30 
88    45 

42.03 
36.78 
31.53 
26.27 

73    00 
73    15 
73    30 
73    45 

351.  71 
346.69 
*    341.68 
336.  65 

81    00 
81     15 
81    30 
81    45 

188.  34 
183.  15 
177.  96 
172.  77 

89    00 
89    15 
89    30 
89    45 

21.02 
15.76 
10.51 
5.26 

100 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  13. — Areas  of  quadrilaterals  of  earth's  surface  of  15'  extent  in  latitude  and 

longitude. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 

square  miles. 

0            /            // 

0    07    30 
0    15    00 
0    22    30 
0    30    00 

297.  02 
297.  02 
297.  02 
297.  01 

0             /           // 

5    37    30 
5    45    00 
5    52    30 
6    00    00 

295.  63 
295.  57 
295.  51 
295.  44 

0              /            // 

11    07    30 
11     15    00 
11    22    30 
11    30    00 

291.  59 
291.  47 
291.  34 
291.  22 

0    37    30 
0    45    00 
0    52    30 
1    00    00 

297.01 
297.00 
296.  99 
296.  98 

6    07    30 
6    15    00 
6    22    30 
6    30    00 

295.  37 
295.  31 
295.  24 
295.17 

11    37    30 
11    45    00 
11     52    30 
12    00    00 

291.09 
290.  96 
290.  83 
290.  70 

1    07    30 
1     15    00 
1    22    30 
1     30    00 

296.97 
296.  96 
296.  94 
296.  93 

6    37    30 
6    45    00 
6    52    30 

7    00    00 

295.  09 
295.  02 
294.  95 
294.  87 

12    07    30 
12    15    00 
12    22    30 
12    30    00 

290.  57 
290.  44 
290.  30 
290.  17 

1    37    30 
1    45    00 
1    52    30 
2    00    00 

296.  91 
296.  89 
296.  87 
296.  85 

7    07    30 
7    15    00 
7    22    30 
7    30    00 

294.  79 
294.  71 
294.  63 
294.  55 

12    37    30 
12    45    00 
12    52    30 
13    00    00 

290.  03 
289.  89 
289.  75 
289.  61 

2    07    30 
2    15    00 
2    22    30 
2    30    00 

296.  82 
296.  80 
296.  77 
296.  75 

7    37    30 
7    45    00 
7    52    30 
8    00    00 

294.  47 
294.  39 
294.  30 
294.  21 

13    07    30 
13     15    00 
13    22    30 
13    30    00 

289.  47 
289.  33 
289.  18 
289.  03 

2    37    30 
2    45    00 
2    52    30 
3    00    00 

296.  72 
296.  69 
296.  66 
296.  63 

8    07    30 
8    15    00 
8    22    30 
8    30    00 

294.  12 
294.  03 
293.  94 
293.  85 

13    37    30 
13    45    00 
13    52    30 
14    00    00 

288.  88 
288.  73 
288.  58 
288.  43 

3    07    30 
3    15    00 
3    22    30 
3    30    00 

296.  60 
296.  56 
296.  53 
296.  49 

8    37    30 
8    45    00 
8    52    30 
9    00    00 

293.  75 
293.  66 
293.  56 
293.  47 

14    07    30 
14    15    00 
14    22    30 
14    30    00 

288.  28 
288.  12 
287.  96 
287.  81 

3    37    30 
3    45    00 
3    52    30 
4    00    00 

296.  45 
296.  41 
296.  36 
296.  32 

9    07    30 
9    15    00 
9    22    30 
9    30    00 

293.  37 
293.  27 
293.  16 
293.  06 

14    37    30 
14    45    00 
14    52    30 
15    00    00 

287.  65 
287.  49 
287.  33 
287.  17 

4    07    30 
4    15    00 
4    22    30 
4    30    00 

296.  28 
296.  23 
296.  18 
296.  13 

9    37    30 
9    45    00 
9    52    30 
10    00    00 

292.  95 
292.  85 
292.  74 
292.  63 

15    07    30 
15     15    00 
15    22    30 
15    30    00 

287.  00 
286.  83 
286.  67 
286.  50 

4    37    30 
4    45    00 
4    52    30 
5    00    00 

296.  08 
296.  03 
295.  98 
295.  93 

10    07    30 
10    15    00 
10    22    30 
10    30    00 

292.  52 
292.  41 
292.30 
292.  19 

15    37    30 
15    45    00 
15    52    30 
16    00    00 

286.  33 
286.  16 
285.  99 
285.  82 

5    07    30 
5    15    00 
5    22    30 
5    30    00 

295.  87 
295.  81 
295.  75 
295.  69 

10    37    30 
10    45    00 
10    52    30 
11    00    00 

292.07 
291.95 
291.  83 
291.  71 

16    07    30 
16    15    00 
16    22    30 
16    30    00 

285.  64 
285.  46 
285.  28 
285.  10 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


101 


TABLE  13. — Areas  of  quadrilaterals  of  earth's  surface  of  15f  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 

square  miles. 

0             /            // 

16    37    30 
16    45    00 
16    52    30 
X7    00    00 

284.  92 
284.  74 
284.  56 
284.38 

0             /            // 

22    07    30 
22    15    00 
22    22    30 
22    30    00 

275.  68 
275.  44 
275.  20 
274.96 

0              /             // 

27     37     30 
27    45    00 
27    52     30 

28    00    00 

263.  93 
263.  64 
263.  34 
263.  04 

17    07    30 
17    15    00 
17    22    30 
17    30    00 

'  284.  19 
284.00 
283.  81 
283.  62 

22    37    30 
22    45    00 
22    52    30 

23    00    00 

274.  72 
274.47 
274.  22 
273.  98 

28    07     30 
28     15    00 
28    22    30 
28    30    00 

262.  74 
262.  44 
262.  14 
261.  84 

17    37    30 
17    45    00 
17    52    30 

18    00    00 

283.  43 
283.  24 
283.  05 
282.  86 

23    07    30 
23    15    00 
23    22    30 
23    30    00 

273.  73 
273.  48 
273.  23 
272.  98 

28    37    30 
28    45    00 
28    52    30 
29    00    00 

261.  53 
261.  23 
260.  92 
260.  61 

18    07    30 
18    15    00 
18    22    30 
18    30    00 

282.66 
282.46 
282.  26 
282.  06 

23    37    30' 
23    45    00 
23    52    30 

24    00    00 

272.  72 
272.  47 
272.  21 
271.  95 

29    07    30 
29    15    00 
29    22    30 
29    30    00 

260.  30 
259.  99 
259.68 
259.  37 

18    37    30 
18    45    00 
18    52    30 
19    00    00 

281.86 
281.  66 
281.  45 
281.  25 

24    07     30 
24    15    00 
24    22    30 
24    30    00 

371.69 
271.44 
271.  17 
270.  91 

29    37    30 
29    45    00 
29    52    30 
30    00    00 

259.  05 
258.  74 
258.  42 
258,  10 

19    07    30 
19    15    00 
19    22    30 
19    30    00 

281.04 
280.  83 
280.  62 
280.41 

24    37    30 
24    45    00 
24    52    30 
25    00    00 

270.65 
270.  38 
270.  11 
269.  85 

30    07    -30 
30    15    00 
30    22    30 
30    30    00 

257.  78 
257.  46 
357.  14 
256.  82 

19    37    30 
19    45    00 
19    52    30 
20    00    00 

280.  20 
279.99 
279.  77 
279.  55 

25    07    30 
25    15    00 
25    22    30 
25    30    00 

269.  58 
269.  31 
269.04 
268.  76 

30    37    30 
30    45    00 
30    52    30 
31    00    00 

256.  49 
256.  17 
255.  84 
255.  52 

20    07    30 
20    15    00 
20    22    30 
20    30    00 

279.34 
279.  12 

278.  90 
278.  68 

25    37    30 
25    45    00 
25    52    30 

26    00    00 

268.  49 
268.  21 
267.  94 
267.  66 

31    07    30 
31     15    00 
31    22    30 
31     30    00 

255.19 
254.  86 
254.  53 
254.  19 

20    37    30 
20    45    00 
20    52    30 

21     00    00 

278.  46 
278.  23 
278.00 
277.  78 

26    07    30 
26    15    00 
26    22    30 
26    30    00 

267.  38 
267.  10 
266.  82 
266.54 

31     37    30 
31    45    00 
31     52    30 
32    00    00 

253.  86 
253.  53 
253.  19 
252.  85 

21    07    30 
21     15    00 
21    22    30 
21     30    00 

277.55 
277.  32 
277.09 
276.  86 

26    37    30 
26    45    00 
26    52    30 

27    00    00 

266.  25  • 
265.  97 
265.  68 
265.  39 

32    07    30 
32    15    00 
32    22    30 
32    30    00 

252.  51 
252.  17 
251.83 
251.  49' 

21    37    30 
21    45    00 
21     52    30 

22    00    00 

276.  63 
276.  39 
276.  16 
275.  92 

27    07    30 
27     15    00 
27    22    30 

27    30    00 

265.  10 
264.81 
264.52 
264.  23 

32    37    30 
32    45    00 
32    52    30 
33    00    00 

251.  15 
250.  80 
250.  45 
250.  11 

102 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  13. — Areas  of  quadrilaterals  of  earth's  surface  of  15'  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilateral. 

•   Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

o         /         // 

33    07    30 
33    15    00 
33    22    30 
33    30    00 

249.  76 
249.  41 
249.  06 
248.  71 

0              /               // 

38     37     30 
38     45     00 
38     52     30 
39    00    00 

233.  28 
232.  88 
232.  48 
232.  07 

o         /          // 

44    07     30 
44     15     00 
44    22     30 
44    30    00 

214.  61 
214.  17 
213.  72 
213.  27 

33    37    30 
33    45    00 
33    52    30 
34    00    00 

248.  36 
248.  00 
247.  65 
247.  29 

39    07     30 
39     15    00 
39    22    30 
39    30    00 

231.  67 
231.  27 
230.  86 
230.  45 

44     37'  30 
44    45     00 
44    52    30 
45     00    00 

212.  82 
212.37 
211.91 
211.  46 

34    07    30 
34    15    00 
34    22    30 
34    30    00 

246.  93 
246.  57 
246.  21 
245.  85 

39    37    30 
39    45    00 
39    52    30 
40    00    00 

230.  04 
229.  63 
229.  22 

228.  81 

45    07     30 
45     15    00 
45     22    30 
45     30    00 

211.00 
210.  55 
210.  09 
209.  63 

34    37    30 
34.45    00 
34    52    30 
35    00    00 

245.  49 
245.  13 
244.  76 
244.  40 

40    07     3tf 
40     15    00 
40    22    30 
40    30    00 

228.  40 
227.  99 
227.  57 

227.  15 

45    37    30 
45     45     00 
45    52    30 
46    00    00 

209.17 

208.  71 
208.  25 
207.  78 

35    07    30 
35     15    00 
35    22    30 
35    30    00 

244.  03 
243.  66 
243.  29 
242.  92 

40    37     30 
40    45    00 
40    52    30 
41     00    00 

226.  73 
226.  32 
225.  90 
225.  48 

46    07     30 
46     15    00 
46    22    30 
46     30    00 

207.  32 
206.  86 
206.  39 
205.  92 

35    37     30 
35    45    00 
35    52    30 
36    00    00 

242.  55 
242.  18 
241.  80 
241.  43 

41     07     30 
41     15    00 
41     22    30 
41     30    00 

225.  06 
224.  64 
224.  21 
223.  79 

46     37     30  • 
46    45     00 
46    52     30 
47     00    00 

205.  45 
204.  99 
204.  52 
204.  05 

36    07    30 
36    15    00 
36    22    30 
36    30    00 

241.  05 
240.  67 
240.  29 
239.  91 

41     37     30 
41     45    00 
41     52    30 
42     00    00 

223.  36 
222.  93 
222.  50 
222.  08 

47    07    30 
47     15    00 
47     22     30 
47     30    00 

203.  57 
203.  10 
202.  63 
202.15 

36    37    30 
36    45    00 
36    52    30 
37    00    00 

239.  53 
239.  15 

238.  77 
238.  38 

42     07     30 
42     15    00 
42    22     30 
42     30    00 

221.  65 
221.  21 
220.  78 
220.  35 

47     37    30 
47    45    00 
47     52     30 
48    00    00 

201.  67 
201.  20 
200.  72 
200.24 

37    07    30 
37     15    00 
37    22    30 
37    30    00 

237.  99 
237.  61 
237.22 
236.  83 

42     37     30 
42    45     00 
42     52     30 
43    00    00 

219.  91 
.  219.  48 
219.  04 
218.  60 

48    07     30 
48     15    00 
48    22    30 
48     30    00 

199.  76 
199.  28 
198.  80 
198.  32 

37    37    30 
37    45    00 
37    52    30 

38    00    00 

236.  44 
236.  05 
235.  66 
235.  26 

43    07     30 
43    15    00 
43     22     30 
43     30    00 

218.  16 
217.73 
217.  28 
216.  84 

48     37     30 
48    45     00 
48    52     30 
49    00    00 

197.  83 
197.  35 
196.  86 
196.  38 

38    07    30 
38    15    00 
38    22    30 
38    30    00 

234.  87' 
234.  47 
234.  07 
233.  68 

43     37     30 
43    45     00 
43    52     30 
44    00    00 

216.  40 
215.  96 
215.  51 
215.  06 

49    07     30 
49     15    00 
49     22    30 
49     30    00 

195.  89 
195.  40 
194.  91 
194.  42 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


103 


13. — Areas  of  quadrilaterals  of  earth's  surface  of  15f  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

0            /            // 

49    37    30 
49    45    00 
49    52    30 
50    00    00 

193.  93 
193.44 
192.  94 
192.  45 

0            /            // 

55    07    30 
55    15    00 
55    22    30 
55    30    00 

171.  39 
170.  86 
170.  33 
169.  79 

0             /             // 

60    37    30 
60    45    00 
60    52    30 
61     00    00. 

147.  21 
146.  64 
146.  07 
145.  50 

50    07    30 
50    15    00 
50    22    30 
50    30    00 

191.95 
191.  46 
190.  96 
190.  46 

55    37    30 
55    45    00 
55    52    30 
56    00    00 

169.  26 
168.  72 
168.  19 
167.65 

61    07    30 
61     15    00 
61     22    30 
61     30    00 

144.  93 
144.  36 
143.  79 
143.  22 

50    37    30 
50    45    00 
50    52    30 

51    00    00 

189.  96 
189.46 
188.  96 
188.  46 

56    07     30 
56    15    00 
56    22    30 
56    30    00 

167.  11 
166.  57 
166.  03 
165.  49 

61    37    30 
61    45    00 
61    52    30 
62    00    00 

142.  65 
142.  08 
141.50 
140.  93 

51    07    30 
51     15    00 
51    22    30 
51    30    00 

187.  96 
187.  46 
186.  95 
186.  45 

56    37    30 
56    45    00 
56    52    30 

57    00    00 

164.95 
164.41 
163.  87 
163.  32 

62    07    30 
62    15    00 
62    22    30 
62    30    00 

140.  35 
139.  78 
139.  20 
138.  62 

51    37    30 
51    45    00 
51    52    30 
52    00    00 

185.94 
185.43 
184.92 
184.41 

57    07    30 
57    15    00 
57    22    30 
57    30    00 

162.  78 
162.  23 
161.68 
161.  14 

62    37    30 
62    45    00 
62    52    30 
63    00    00 

138.  04 
137.  47 
136.  89 
136.  31 

52    07     30 
52    15    00 
52    22    30 
52    30    00 

183.90 
183.39 
182.  88 
182.  37 

57    37    30 
57    45    00 
57    52    30 

58    00    00 

160.59 
160.04 
159.  49 
158.  94 

63    07    30 
63    15    00 
63    22    30 
63    30    00  ^ 

135.  73 
135.  15 
134.  56 
133.  98 

52    37    30 
52    45    00 
52    52    30 
53    00    00 

181.  85 
181.  34 
180.  82 
180.  31 

58    07    30 
58    15    00 
58    22    30 
58    30    00 

158.  39 
157.  84 
157.  29 
156.  73 

63    37    30 
63    45    00 
63    52    30 
64    00    00 

133.  40 
132.  81 
132.  23 
131.64 

53    07    30 
53    15    00 
53    22    30 
53    30    00 

179.  79 
179.  27 
178.  75 
178.  23 

58    37    30 
58    45    00 
58    52    30 
59    00    00 

156.  18 
155.  62 
155.  07 
154.  51 

64    07     30 
64     15    00 
64    22    30 
64    30    00 

131.06 
130.  47 
129.  88 
129.  29 

53    37    30 
53    45    00 
53    52    30 

54    00    00 

177.  71 
177.  19 
176.67 
176.  14 

59    07    30 
59    15    00 
59    22    30 
59    30    00 

153.  96 
153.  40 
152.  84 
152.  28 

64    37     30 
64    45    00 
64    52    30 
65    00    00 

128.  70 
128.  12 
127.  53 
126.  94 

54    07     30 
54     15    00 
54    22    30 
54    30    00 

175.  62 
175.  10 
174.  57 
174.04 

59    37    30 
59    45    00 
59    52    30 
60    00    00 

151.  72 
151.  16 
150.  60 
150.  03 

65    07    30 
65    15    00 
65    22    30 
65    30    00 

126.  34 
125.  75 
125.  16 
124.  57 

54    37    30 
54    45    00 
54    52    30 

55    00    00 

173.  51 
172.99 
172.  46 
171.93 

60    07    30 
60     15    00 
60    22    30 
60    30    00 

149.  47 
148.  91 
148.  34 
147.  77 

65    37    30 
65    45    00 
65    52    30 
66    00    00 

123.  97 
123.  38 
122.  .78 
122.  19 

104 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  13. — Areas  of  quadrilaterals  of  earth's  surface  of  15f  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 

square  miles. 

0             /             // 

66    07    30- 
66    15    00 
66    22    30 
66    30    00 

121.59 
120.  99 
120.  40 
119.  80 

o        /        // 

71     37    30 
71     45    00 
71     52    30 
72    00    00 

94.78 
94.16 
93.54 
92.92 

0              /            // 

77    07    30 
77     15    00 
77    22    30 
77    30    00 

67.04 
66.41 
65.77 
65.13 

66    37    30 
66    45    00 
66    52    30 
67    00    00 

119.  20 
118.  60 
118.00 
117.40 

72    07    30 
72    15    00 
72    22    30 
72    30    00 

92.  30 
91.68 
91.05 
90.43 

77    37    30 
77    45    00 
77    52    30 
78    00    00 

64.49 
63.85 
63.20 
62.56 

67    07    30 
67     15    00 
67    22    30 
67    30    00 

116.  80 
116.20 
115.  59 
114.  99 

72    37    30 
72    45    00 
72    52    30 
73    00    00 

89.80 
89.18 
88.  55 
87.93 

78    07    30 
78     15    00 
78    22    30 
78    30    00 

61.92 
61.28 
60.64 
60.00 

67    37    30 
67    45    00 
67    52    30 
68    00    00 

114.  39 
113.  78 
113.  18 
112.  57 

73    07    30 
73     15    00 
73    22    30 
73    30    00 

87.30 
86.67 
86.05 
85.42 

78    37    30 
78    45    00 
78    52    30 
79    00    00 

59.35 
58.71 
58.06 
57.42 

68    07    30 
68     15    00 
68    22    30 
68    30    00 

111.97 
111.  36 
110.  76 
110.  15 

73    37    30 
73    45    00 
73    52    30 

74    00    00 

84.79 
84.16 
83.53 
82.91 

79    07    30 
79    15    00 
79    22    30 
79    30    00 

56.78 
56.13 
55.49 
54.84 

68    37    30 
68    45    00 
68    52    30 
69    00    00 

109.  54 
108.  93 
108.  32 
107.  71 

74    07    30 
74    15    00 
74    22    30 
74    30    00 

82.28 
81.65 
81.01 
80.38 

79    37    30 
79    45    00 
79    52    30 
80    00    00 

54.20 
53.55 
52.91 
52.26 

69    07    30 
69    15    00 
69    22    30 
69    30    00 

107.  10 
106.  49 
105.  88 
105.  27 

74    37    30 
74    45    00 
74    52    30 
75    00    00 

79.75 
79.12 
78.49 
77.86 

80    07    30 
80    15    00 
80    22    30 
80    30    00 

51.62 
50.97 
50.32 
49.68 

69    37    30 
69    45    00 
69    52    30 
70    00    00 

104.  65 
104.  04 
103.  43 
102.  81 

75    07    30 
75    15    00 
75    22    30 
75    30    00 

77.22 
76.59 
75.95 
75.32 

80    37    30 
80    45    00 
80    52    30 
81    00    00 

49.03 
48.38 
47.73 
47.08 

70    07    30 
70    15    00 
70    22    30 
70    30    00 

102.  20 
101.59  . 
100.97 
100.35 

75    37    30 
75    45    00 
75    52    30 
76    00    00 

74.69 
74.05 
73.42 

72.78 

81     07    30 
81     15    00 
81    22    30 
81     30    00 

46.44 
45.79 
45.14 
44.49 

70    37    30 
70    45    00 
70    52    30 
71    00    00 

99.74 
99.12 
98.50 

97.88 

76    07    30 
76    15    00 
76    22    30 
76    30    00 

72.  14 
71.51 
70.87 
70.24 

81    37    30 
81    45    00 
81    52    30 
82    00    00 

43.84 
43.19 
42.54 
41.89 

71    07    30 
71     15    00 
71    22    30 
71     30    00 

97.26 
96.65 
96.03 
95.41 

76    37    30 
76    45    00 
76    52    30 

77    00    00 

69.60 
68.96 
68.32 

67.68 

82    07    30 
82    15    00 
82    22    30 
82    30    00 

41.24 
40.59 
39.94 
39.29 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


105 


TABLE  13. — Areas  of  quadrilaterals  of  earth's  surface  of  15'  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  latitude 
of  quadrilateral. 

Area  in 
square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 

square  miles. 

Middle  latitude 
of  quadrilateral. 

Area  in 

square  miles. 

o          /         // 

0            /            // 

0             /            // 

82    37    30 
82    45    00 
82    52    30 
83    00    00 

38.64 
37.99 
37.34 
36.69 

85    07    30 
85    15    00 
85    22    30 
85    30    00 

25.58 
24.93 
24.27 
23.62 

87    37    30 
87    45    00 
87    52    30 
88    00    00 

12.48 
11.82 
11.16 
10.51 

83    07    30 
83    15    00 
83    22    30 
83    30    00 

36.03 
35.  38 
34.73 
34.08 

85    37    30 
85    45    00 
85    52    30 
86    00    00 

22.97 
22.31 
21.66 
21.00 

88    07    30 
88    15    00 
88    22    30 
88    30    00 

9.85 
9.20 
8.54 
7.88 

83    37    30 
83    45    00 
83    52    30 
84    00    00 

33.42 
32.77 
32.12 
31.47 

86    07*  30 
86    15    00 
86    22    30 
86    30    00 

20.35 
19.69 
19.04 
18.38 

88    37    30 
88    45    00 
88    52    30 
89    00    00 

7.22 
6.57 
5.91 
5.26 

84    07    30 
84     15    00 
84    22    30 
84    30    00 

30.81 
30.  16 
29.51 

28.86 

86    37    30 
86    45    00 
86    52    30 
87    00    00 

17.72 
17.07 
16.41 
15.76 

89    07    30 
89    15    00 
89    22    30 
89    30    00 

4.60 
3.94 
3.28 
2.63 

84    37    30 
84    45-  00 
84    52    30 
85    00    00 

28.20 
27.54 
26.89 
26.24 

87    07    30 
87    15    00 
87    22    30 
87    30    00 

15.10 
14.44 
13.79 
.      13.  13 

'89    37    30 
89    45    00 
89    52    30 

1.97 
1.31 

0.66 

106 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  14.—  Areas  of  quadrilaterals  of  earth's  surface  of  10'   extent  in  latitude  and 

longitude. 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadri  lateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

o        / 

0    05 
0    15 
0    25 
0    35 

132.  01 
132.01 
132.  01 
132.  00 

0            / 

7    25 
7    35 
7    45 
7    55 

130.  93 
130.  88 
130.  84 
130.  79 

o          / 

14     45 
14    55 
15    05 
15     15 

127.  77 
127.  67 
127.  58 
127.  48 

0    45 
0    55 
1    05 
1     15 

132.00 
131.99 
131.  99 

131.98 

8    05 
8    15 
8    25 
8    35 

130.  73 
130.  68 
130.  63 
130.57 

15    25 
15    35 
15    45 
15    55 

'    127.38 
127.  28 
127.  18 
127.  08 

1     25 
1     35 
1    45 
1     55 

131.97 
131.  96 
131.95 
131.  94 

8    45 
8    55 
9    05 
9    15 

130.  51 
130.  46 
130.  40 
130.  34 

16    05  - 
16     15 
16    25 
16    35 

126.98 
126.  87 
126.  77 
126.66 

2    05 
2     15 
2    25 
2    35 

131.  93 
131.91 
131.  90 
131.  88 

9    25 
9    35 
9    45 
9    55 

130.  28 
130.  22 
130.  15 
130.  09 

16    45 
16    55 
17    05 
17     15 

126.55 
126.  44 
126.  33 
126.22 

2    45 
2    55 
3    05 
3     15 

131.  86 
131.  84 
131.  82 
131.  80 

10    05 
10     15 
10    25 
10    35 

130.  02 
129.  96 
129.  89 
129.  82 

17    25 
17    35 
17    45 
17    55 

126.  11 
126.  00 
125.  88 
125.  77 

3    25 
3    35 
3    45 
3    55 

131.  78 
131.  76 
131.  74 
131.  71 

10    45 
10    55 
11    05 
11     15 

129.  76 
129.68 
129.  61 
129.54 

18    05 
18    15 
18    25 
18    35 

125.  65 
125.  54 
125.  42 
125.  30 

4    05 
4    15 
4    25 
4    35 

131.  68 
131.  66 
131.  63 
131.60 

11     25 
11     35 
11     45 
11     55 

129.  47 
129.  39 
129.  32 
129.  24 

18    45 
18    55 
19    05 
"19     15 

125.  18 
125.  06 
124.  94 
124.  81 

4    45 
4    55 
5    05 
5     15 

131.57 
131.  54 
131.  50 
131.47 

12    05 
12     15 
12    25 
12    35 

129.  16 
129.  08 
129.  00 
128.  92 

19    25 
19    35 
19    45 
19    55 

124.  69 
124.  56 
124.  44 
124.  31 

5    25 
5    35 
5    45 
5    55 

131.  44 
131.  40 
131.  36 
131.  33 

12     45 
12    55 
13    05 
13     15 

128.  84 
128.76 
128.  67 
128.  59 

20    05 
20    15 
20    25 
20    35 

124.  18 
124.  05 
123.  92 
123.  79 

6    05 
6    15 
6    25 
6    35 

131.  29 
131.  25 
131.21 
131.16 

13    25 
13    35 
13    45 
13    55 

128.  50 
128.  41 
128.  33 
128.  24 

20    45 
20    55 
21    05 
21     15 

123.  66 
123.  52 
123.  39 
123.  25 

6    45 
6    55 

7    05 
7     15 

131.  12 
131.  07 
131.  03 

130.  98 

14    05 
14    15 
14    25 
14    35 

128.  14 
128.  05 
127.  96 
127.  87 

21     25 
21    35 
21    45 
21    55 

123.  12 
122.  98 
122.  84 
122.  70 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


107 


TABLE  14.— Areas  of  quadrilaterals  of  earth's  surface  of  10'  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

! 

0              / 

0              / 

o          / 

22    05 

122.  56 

29    25 

.  115.  37 

36    45 

106.  29 

22     15 

122.  42 

29    35 

115.  18 

36    55 

106.  06 

22    25 

122.  28 

29    45 

114.99 

37    05 

105.  83 

22    35 

122.  13 

29    55 

114.  81 

37    15 

105.  60 

22    45 

121.  99 

30    05 

114.  62 

37    25 

105.  37 

22    55 

121.84 

30    15 

114.  43 

37    35 

105.  14 

23    05 

121.  69 

30    25 

114.  24 

37    45 

104.  91 

23    15 

121.  55 

30    35 

114.  04 

37    55 

104.68 

23    25 

121.40 

30    45 

113.  85 

38    05 

104.44 

23    35 

121.  25 

30    55 

113.  66 

38    15 

104.  21 

23    45 

121.  10 

31    05 

113.  47 

38    25 

103.  97 

23    55 

120.  94 

31     15 

113.  27 

38    35 

103.  74 

24    05 

120.  79 

31    25 

113.07 

38    45 

103.  50 

24    15 

120.  64 

31    35 

112.  88 

38    55 

103.  26 

24    25 

120.  48 

31    45 

112.  68 

39    05 

103.  02 

24    35 

120.  33 

31    55 

112.  48 

39    15 

102.  78 

24    45 

120.  17 

32    05            112.28 

39    25 

102.  54 

24    55 

120.  01 

32    15 

112.  08 

39    35 

102.  30 

25    05 

119.  85 

32    25 

111.  87 

39    45 

102.  06 

25    15 

119.  69 

32    35 

111.67 

39    55 

101.  82 

25    25 

119.  53 

32    45 

111.47 

40    05 

101.  57 

25    35 

119.  37 

32    55 

111.26 

40    15 

101.33 

25    45 

119.  21 

33    05 

111.06 

40    25 

101.08 

25    55 

119.04 

33    15 

110.  85 

40    35 

100.83 

26    05 

118.  87 

33    25 

110.64 

40    45 

100.59 

26    15 

118.71 

33    35 

110.43 

40    55 

100.34 

26    25 

118.54 

33    45 

110.  22 

41    05 

100.  09 

26    35 

118.  37 

33    55 

110.  01 

41     15 

99.84 

26    45 

118.  21 

34    05 

109.80 

41     25 

99.59 

26    55 

118.04 

34    15 

109.  59 

41     35 

99.33 

27    05 

117.  87 

34    25 

109.  37 

41     45 

99.08 

27    15 

117.  69 

34    35 

109.16 

41     55 

98.83 

27    25 

117.52 

34    45 

108.  94 

42    05 

98.57 

27    35 

117.35 

34    55 

108.  73 

42    15 

98.32 

27    45 

117.17 

35    05 

108.  51 

42    25 

98.06 

27    55 

116.99 

35    15 

108.  29 

42    35 

97.80 

28    05 

116.82 

35    25 

108.  07 

42    45 

97.55 

28    15 

116.64 

35    35 

107.  85 

42    55 

97.29 

28    25 

116.  46 

35    45 

107.  63 

43    05 

97.  03 

28    35     i         116.28 

35    55 

107.  41 

43     15 

96.77 

28    45 

116.  10 

36    05 

107.  19 

43    25 

96.50 

28    55 

115.  92 

36    15 

106.  96 

43    35 

96.24 

29    05 

115.  73 

36    25 

106.74 

43    45 

95.98 

29     15 

115.  55 

36    35 

106.  51 

43    55 

95.71 

108 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  14. — Areas  of  quadrilaterals  of  earth's  surface  of  10'  extent  in  latitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

o        / 

44    05 
44     15 
44    25 
44    35 

95.45 
95.19 
94.92 
94.65 

0             / 

50    45 
50    55 
51    05 

51     15 

84.21 
83.91 
83.61 
83.31 

0            / 

57    25 
57    35 
57    45 
57    55 

71.78 
71.46 
71.13 

70.80 

-44    45 
44    55 
45    05 
45     15 

94.38 
94.11 
93.84 
93.58 

51     25 
51     35 
51    45 
51    55 

83.01 
82.71 
82.41 
82.11 

58    05 
58    15 
58    25 
58    35 

70.48 
70.15 
69.82 
69.49 

45     25 
45     35 
45    45 
45    55 

93.30 
93.03 
92.76 
92.48 

52    05 
52     15 
52    25 
52    35 

81.81 
81.51 
81.20 
80.90 

58    45 
58    55 
59    05 
59    15 

69.  17 
68.84 
68.51 
68.18 

46    05 
46    15 
46    25 
46    35 

92.21 
91.94 
91.66 
91.38 

52    45 
52    55 
53    05 
53    15 

80.60 
80.29 
79.98 
79.68 

59    25 
59    35 
59    45 
59    55 

67.84 
67.51 
67.18 
66.85 

46    45 
46    55 
47     05 
47     15 

91.10 
90.82 
90.55 
90.27 

53    25 
53    35 
53    45 
53    55 

79.37 
79.06 

78.75 
78.44 

60    05 
,60    15 
60    25 
60    35 

66.51 
66.18 
65.84 
65.51 

47    25 
47    35 
47    45 
47    55 

89.99 
89.70 
89.42 
89.14  . 

54    05 
54    15 
54    25 
54    35 

78.13 
77.82 
77.51 
77.19 

60    45 
60    55 
61    05 
61     15 

65.17 
64.84 
64.50 
64.16 

48    05 
48    15 
48    25 
48    35 

88.85 
88.57 
88.28 
88.00 

54    45 
54    55 
55    05 
55     15 

76.88 
76.57 
76.25 
75.94 

61    25 
61     35 
61     45 
61    55 

63.82 
63.48 
63.14 
62.80 

48    45 
48    55 
49    05 
49     15 

87.71 
87.42 
87.13 
86.84 

55    25 
55    35 
55    45 
55    55 

75.62 
75.30 
74.99 
74.67 

62    05 
62    15 
62    25 
62    35 

62.46 
62.12 
61.78 
61.44 

49    25' 
49    35 
49    45 
49    55 

86.55 
86.26 
85.97 
85.68 

56    05 
56    15 
56    25 
56    35 

74.35 
74.03 
73.71 
73.39 

62    45 
62    55 
63    05 
63    15 

61.10 
60.75 
60.41 
60.06 

50    05 
50    15 
50    25 
50    35 

85.39 
85.09 
84.80 
84.50 

56    45 
56    55 
57    05 

57    15 

73.07 
72.75 
72.43 
72.10 

63    25 
63    35 
63    45 
63    55 

59.72 
59.37 
59.03 

58.68 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


109 


TABLE  14.—  Areas  of  quadrilaterals  of  earth's  surface  of  10'  extent  inlalitude  and  longi- 
tude— Continued. 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

o         / 

64    05 
64     15 
64    25 
64    35 

58.33 
57.99 
57.64 
57.29 

o        / 

70    45 
70    55 
71    05 
71     15 

44.05 
43.69 
43.32 
42.95 

0             / 

77    25 
77    35 
77    45 
77    55 

29.13 
28.76 
28.37 
27.99 

64    45 
64    55 
65    05 
65    15 

56.94 
56.59 
56.24 
55.89 

71    25 
71    35 
71    45 
71    55 

42.58 
42.22 
41.85 
41.48 

78    05 
78    15 
78    25 
78    35 

27.62 
27.24 
26.85 
26.47 

65    25 
65    35 
65    45 
65    55 

55.54 
55.19 
54.83 
54.48 

72    05 
72    15 
72    25 
72    35 

41.11 
40.74 
40.37 
40.00 

78    45 
78    55 
79    05 
79    15 

26.09 
25.71 
25.33 
24.95 

66    05 
66    15 
66    25 
66    35 

54.13 
53.78 
53.42 
53.06 

72    45 
72    55 
73    05 
73    15 

39.63   . 
39.26 

38.89 
38.52 

79    25 
79    35 
79    45 
79    55 

24.57 
24.18 
23.80 
23.42 

66    45 
66    55 
67    05 
67    15 

52.71 
52.35 
52.00 
51.64 

73    25 
73    35 
73    45 
73    55 

38.  15 
37.78 
37.  41  • 
37.03 

80    05 
80     15 
80    25 
80    35 

23.04 
22.65 
22.27 
21.89 

67    25 
67    35 
67    45 
67    55 

51.28 
50.93 
50.57 
50.21 

74    05 
74    15 
74    25 
74    35 

36.66 
36.29 
35.91 
35.54 

80    45 
80    55 
81    05 
81     15 

21.50 
21.12 
20.73 
20.35 

68    05 
68    15 
68    25 
68    35 

49.85 
49.49 
49.13 

48.77 

74    45 
74    55 
75    05 
75    15 

35.17 
04.79 
34.42 
34.04 

81    25 
81    35 
81    45 
81    55 

.   19.97 
19.58 
19.20* 
18.81 

68    45 
68    55 
69    05 
69     15 

48.41 
48.05 
47.69 
47.33 

75    25 
75    35 
75    45 
75    55 

33.66 
33.29 
32.91 
32.53 

82    05 
82    15 
82    25 
82    35 

18.43 
18.04 
17.65 
17.27 

69    25 
69    35 
69    45 
69   -55 

46.97 
46.60 
46.24 
45.88 

76    05 
76    15 
76    25 

76.    35 

32.16 
31.78 
31.40 
31.03 

82    45 
82    55 
83    05 
83    15 

16.88 
16.50 
16.11 
15.73 

70    05 
70    15 
70    25 
70    35 

45.51 
45.15 
44.78 
44.42 

76    45 
76    55 

77    05 
77    15 

30.65 
30.27 
29.89 
29.51 

83    25 
83    35 
83    45 
83    55 

15.34 
14.95 
14.57 
14.18 

110 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  14. — Areas  of  quadrilaterals  of  earth's  surface  of  10'  extent  in  latitude  and  longi- 
tude— Continued . 

[From  Smithsonian  Geographical  Tables.] 


Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

Middle  lati- 
tude of 
quadrilateral. 

Area  in  square 
miles. 

o        / 

0            / 

0             / 

84    05 

13.79 

86    05 

9.14 

88    05 

4.47 

84    15 

13.40 

86    15 

8.75 

88    15 

.        4.09 

84    25 

13.02 

86    25 

8.36 

88    25 

3.70 

84    35 

12.63 

86    35 

7.97 

88    35 

3.31 

84    45 

12.24 

86    45 

7.59 

88    45 

2.92 

84    55 

11.  86 

86    55 

7.20 

88    55 

2.53 

85    05 

11.47 

87    05 

6.81 

89    05 

2.14 

85    15 

11.08 

87    15 

6.42 

89     15 

1.75 

85    25 

10.69 

87    25 

6.03 

89    25 

1.36 

85    35 

10.30 

87    35 

5.64 

89    35 

0.97 

85    45 

9.92 

87    45 

5.25 

89    45 

0.58 

85    55 

9.53 

87    55 

4.86 

89    55 

0.19 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  15. — For  conversion  of  arc  into  time. 


Ill 


o 

h.  m. 

o 

60 

61 
62 
63 
64 
65 
66 
67 
68 
69 

h.  m. 

o 

120 

121 
122 
123 
124 
125 
126 
127 
128 
129 

h.  m. 

o 

h.  m. 

0 

h.  m. 

o 

h.  m. 

' 

m.  s. 

" 

s. 

0 

1 

2 
3 
4 
5 

6 

7 
8 
9 

0    0 
0    4 
0    8 
012 
0  16 
0  20 
0  24 
0  28 
032 
0  36 

4    0 
4    4 
4    8 
4  12 
4  16 
4  20 
4  24 
4  28 
4  32 
4  36 

8    0 
8    4 
8    8 
8  12 
8  16 
8  20 
8  24 
828 
8  32 
8  36 

180 

181 
182 
183 
184 
185 
186 
187 
188 
189 

12  0 
12  4 
12  8 
12  12 
12  16 
12  20 
12  24 
12  28 
12  32 
12  36 

240 

241 
242 
243 
244 
245 
246 
247 
248 
249 

16    0 
16    4 
16    8 
16  12 
16  16 
16  20 
16  24 
16  28 
16  32 
16  36 

300 

301 
302 
303 
304 
305 
306 
307 
308 
309 

20  0 
20  4 
20  8 
20  12 
20  16 
20  20 
20  24 
20  28 
20  32 
20  36 

0 

1 
2 
3 
4 
5 
6 
7 
8 
9 

0    0 
0    4 
0    8 
0  12 
0  16 
0  20 
0  24 
0  28 
0  32 
0  36 

0 

1 
2 
3 
4 
5 
6 
7 
8 
9 

0.000 
0.067 
0.133 
0.200 
0.267 
0.333 
0.400 
0.467 
0.533 
0.600 

10 

0  40 

70 

440 

130 

8  40 

190 

12  40 

250 

16  40 

310 

20  40 

10 

0  40 

10 

0.667 

11 
12 
13 
14 
15 
16 
17 
18 
19 

0  44 
048 
0  52 
056 
1    0 
1    4 
1    8 
1  12 
1  16 

71 
72 
73 
74 
75 
76 
77 
78 
79 

4  44 
4  48 
452 
4  56 
5    0 
5    4 
5    8 
5  12 
5  16 

131 
132 
133 
134 
185 
136 
137 
138 
139 

844 
8  48 
852 
8  56 
9    0 
9    4 
9    8 
9  12 
9  16 

191 
192 
193 
194 
195 
196 
197 
198 
199 

1244 
12  48 
12  52 
12  56 
13  0 
13  4 
13  8 
13  12 
13  16 

251 
252 
253 
254 
255 
256 
257 
258 
259 

260~ 

16  44 
16  48 
16  52 
16  56 
17    0 
17    4 
17    8 
17  12 
17  16 

311 
312 
313 
314 
315 
316 
317 
318 
319 

20  44 
20  48 
20  52 
20  56 
21  0 
21  4 
21  8 
21  12 
21  16 

11 
12 
13 
14 
15 
16 
17 
18 
19 

0  44 
048 
0  52 
0  56 
1    0 
1    4 
1    8 
i  12 
1  16 

11 
12 
13 
14 
15 
16 
17 
18 
19 

0.733 
0.800 
0.867 
0.933 
1.000 
1.067 
1.133 
1.200 
1.267 

20 

1  20 

80 

5  20 

140 

141 
142 
143 
144 
145 
146 
147 
148 
149 

9  20 

|200 

13  20 

17  20 

320 

21  20 

20 

1  20 

20 

1.333 

21 
22 
23 
24 
25 
26 
27 
28 
29 

~30~ 

31 
3'2 
33 
M 
35 
36 
37 
38 
39 

1  24 
1  28 
1  32 
1  36 
1  40 
1  44 
1  48 
1  52 
1  56 

81 
82 
83 
S4 
s:, 
86 
87 
88 
89 

524 
5  28 
5  32 
5  36 
5  40 
544 
5  48 
5  52 
556 

9  24 
9  28 
9  32 
9  36 
9  40 
944 
9  48 
9  52 
9  56 

201 
202 
203 
204 
205 
206 
207 
208 
209 

13  24 
13  28 
13  32 
13  36 
13  40 
1344 
13  48 
1352 
13  56 

261 
262 
263 
264 
265 
266 
267 
268 
269 

17  24 
17  28 
17  32 
17  36 
17  40 
17  44 
17  48 
17  52 
17  56 

321 
322 
323 
324 
325 
326 
327 
328 
329 

330 

21  24 
21  28 
21  32 
21  36 
21  40 
21  44 
21  48 
21  52 
21  56 

21 
22 
23 
24 
25 
26 
27 
38 
29 

1  24 
1  28 
1  32 
1  36 
1  40 
1  44 
1  48 
1  52 
1  56 

21 
22 
23 
24 
25 
26 
27 
28 
29 

~80~ 

1.400 
1.467 
1.533 
1.600 
1.667 
1.733 
1.800 
1.867 
1.933 

2    0 

90 

6    0 

150 

10    0 

210 

14  0 

270 

18    0 

22  0 

30 

2    0 

2.000 

2    4 
2    8 
2  12 
2  16 
2  20 
2  24 
2  28 
2  32 
2  36 

91 
92 
93 
94 
95 
% 
97 
98 
99 

6    4 
6    8 
6  12 
6  16 
6  20 
6  24 
6  28 
6  32 
6  36 

151 
152 
153 
154 
155 
156 
157 
158 
159 

160~ 

10    4 
10    8 
10  12 
10  16 
10  20 
10  24 
10  28 
10  32 
1036 

211 
212 
213 
214 
215 
216 
217 
218 
219 

220~ 

14  4 
14  8 
14  12 
14  16 
14  20 
14  24 
14  28 
14  32 
1436 

271 
272 
273 
274 
275 
276 
277 
278 
279 

280~ 

18    4 
18    8 
18  12 
18  16 
18  20 
18  24 
18  28 
18  32 
18  36 

331 
332 
333 
334 
335 
336 
337 
338 
339 

22  4 
22  8 
22  12 
22  16 
2220 
22  24 
22  28 
22  32 
22  36 

31 
32 
33 
34 
35 
36 
37 
38 
39 

~4P~ 

2    4 
2    8 
2  12 
2  16 
2  20 
2  24 
2  28 
2  32 
2  36 

31 
32 
33 
34 
35 
36 
37 
38 
39 

2.067 
2.133 
2  200 
2.267 
2.333 
2.400 
2.467 
2.533 
2.600 

40 

2  40 

100 

6  40 

10  40 

14  40 

18  40 

.'{40 

22  40 

2  40 

40 

2.667 

41 
42 
43 
44 
45 
46 
47 
48 
49 

244 
2  48 
2  52 
2  56 
3    0 
3    4 
3    8 
3  12 
3  16 

101 
102 
103 
104 
105 
106 
107 
108 
109 

6  44 
6  48 
6  52 
6  56 
7    0 
7    4 
7    8 
7  12 
7  16 

161 
162 
163 
164 
165 
166 
167 
168 
169 

10  44 
1048 
10  52 
10  56 
11    0 
11    4 
11    8 
11  12 
11  16 

221 
222 
223 
224 
225 
226 
227 
228 
229 

14  44 
14  48 
1452 
14  56 
15  0 
15  4 
15  8 
15  12 
15  16 

281 
282 
283 

284 

285 
•zst; 
287 
288 
289 

18  44 
1848 
18  52 
18  56 
19    0 
19    4 
19    8 
19  12 
19  16 

341 
342 
343 
344 
345 
346 
347 
348 
349 

2244 
22  48 
22  52 
2256 
23  0 
23  4 
23  8 
23  12 
23  16 

41 
42 
43 
44 
45 
46 
47 
48 
49 

2  44 
2  48 
2  52 
2  56 
3    0 
3    4 
3    8. 
3  12 
3  16 

41 
42 
43 
44 
45 
46 
47 
48 
49 

2.733 
2.800 
2,867 
2.933 
3.000 
3.067 
3.133 
3.200 
3.267 

50 

3  20 

110 

7  20 

170 

11  20 

230 

1520 

290 

1920 

350 

23  20 

50 

320 

50 

3.333 

51 
M 
53 
54 
55 
56 
57 
58 
59 

3  24 
3  28 
3  32 
3  36 
340 
3  44 
3  48 
3  52 
3  56 

111 
112 
113 
114 
115 
116 
117 
118 
119 

7  24 
7  28 
7  32 
7  36 
740 
7  44 
748 
7  52 
7  56 

171 
172. 
173 
174 
175 
176 
177 
178 
179 

11  24 
11  28 
11  32 
11  36 
11  40 
11  44 
11  48 
11  52 
11  56 

231 
232 
233 
234 
235 
236 
237 
238 
239 

15  24 
15  28 
15  32 
15  36 
15  40 
15  44 
15  48 
15  52 
15  56 

291 
292 
293 
294 
295 
296 
297 
298 
299 

19  24 
1928 
19  32 
19  36 
19  40 
19  44 
19  48 
19  52 
19  56 

351 
352 
353 
354 
355 
356 
357 
358 
359 

23  24 
23  28 
23  32 
23  36 
23  40 
23  44 
2348 
23  52 
23  56 

61 
52 
53 
54 
55 
56 
57 
58 
59 

3  24 
3  28 
3  32 
3  36 
3  40 
3  44 
3  48 
3  62 
'3  56 

51 
52 
53 
54 
55 
56 
57 
58 
59 

3.400 
3.467 
3.533 
3.600 
3.667 
3.733 
3.800 
3.867 
3.933 

60 

4    0 

120 

8    0 

180 

12    0 

240 

16  0 

300 

.20    0 

360 

24  0 

60 

4    0 

60 

4.000 

112 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  16. — For  conversion  of  time  into  arc. 


Hours  of  time  into  arc. 

Time. 

Arc. 

Time. 

Arc. 

Time.      Arc.  , 

Time. 

Arc. 

Time. 

Arc. 

Time. 

Arc. 

hrs. 

o 

hrs. 

0 

hrs. 

0 

hrs. 

o 

hrs 

o 

hrs. 

0 

1 

15 

5 

75 

9 

135 

13 

195 

1  7 

255 

21 

315 

2 

30 

6 

90 

10 

150 

14 

210 

18 

270 

22 

330 

3 

45 

7 

105 

11 

165 

15 

225 

19 

285 

23 

345 

4 

60 

8 

120 

12 

180 

16 

240 

20 

300 

24 

360 

Minutes  of  time  into  arc. 

Seconds  of  time  into  arc. 

m. 

o     / 

m. 

o     / 

m 

o     / 

s. 

s. 

s. 

1 

0  15 

21 

5  15 

41 

10  15 

1 

0  15 

21 

5  15 

41 

10  15 

•    2 

0  30 

22 

5  30 

42 

10  30 

2 

0  30 

22 

5  30 

42 

10  30 

3 

0  45 

23 

5  45 

43 

10  45 

3 

0  45 

23 

5  45 

43 

10  45 

4 

1    0 

24 

6    0 

44 

11    0 

4 

1     0 

24 

6    0 

44 

11    0 

5 

1  15 

25 

6  15 

45 

11  15 

5 

1  15 

25 

6  15 

45 

11  15 

6 

1  30 

26 

6  30 

46 

11  30 

6 

1  30 

26 

6  30 

46 

11  30 

7 

1  45 

27 

6  45 

47 

11  45 

7 

1  45 

27 

6  45 

47 

11  45 

8 

2    0 

28 

7    0 

48 

12    0 

8 

2    0 

28 

7    0 

48 

12    0 

9 

2  15 

29 

7  15 

49 

12  15 

9 

2  15 

29 

7  15 

49 

12  15 

10 

2  30 

30 

7  30 

50 

12  30 

10 

2  30 

30 

7  30 

50 

12  30 

11 

2  45 

31 

7  45 

51 

12  45 

11 

2  45 

31 

7  45 

51 

12  45 

12 

3    0 

32 

8    0 

52 

13    0 

12' 

3    0 

32 

8    0 

52 

13    0 

13 

3  15 

33 

8  15 

53 

13  15 

13 

3  15 

33 

8  15 

53 

13  15 

14 

3  30 

34 

8  30 

54 

13  30 

14 

3  30 

34 

8  30 

54 

13  30 

15 

3  45 

35 

8  45 

55 

13  45 

15 

3  45 

35 

8  45 

55 

13  45 

16 

4    0 

36 

9    0 

56 

14    0 

16 

4    0 

36 

9    0 

56 

14    0 

17 

4  15 

37 

9  15 

57 

14  15 

17 

4  15 

37 

9  15 

57 

14  15 

18 

4  30 

38 

9  30 

58 

14  30 

18 

4  30 

38 

9  30 

58 

14  30 

19 

4  45 

39 

9  45 

59 

14  45 

19 

4  45 

39 

9  45 

59 

14  45 

20 

5    0 

40 

10    0 

60 

15    0 

20 

5    0 

40 

10    0 

60 

15    0 

Hundredths  of  a  second  of  time  into  arc. 

Hundredths 

of  a  second 

.00 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

of  time. 

„ 

// 

n 

n 

n 

n 

„ 

n 

ii 

ii 

0.00 

0.00 

0.15 

0.30 

0.45 

0.60 

0.75 

0.90 

1.05 

1.20 

1.35 

.10 

1.50 

1.65 

1.80 

1.95 

2.10 

2.25 

2.40 

2.55 

2.70 

2.85 

.20 

3.00 

3.15 

3.30 

3.45 

3.60 

3.75 

3,90 

4.05 

4.20 

4.35 

.30 

4.50 

4.65 

4.80 

4.95 

5.10 

5.25 

5.40 

5.55 

5.70 

5.85 

.40 

6.00 

6.15 

6.30 

6.45 

6.60 

6.75 

6.90      7.05 

7.20 

7.35 

0.50 

7.50 

7.65 

7.80 

7.95 

8.10 

8.25 

8.40 

8.55 

8.70 

8.85 

.60 

9.00 

9.15 

9.30 

9.45 

9.60 

9.75 

9.90 

10.05 

10.20 

10.35 

.70 

10.50 

10.65 

10.80 

10.95 

11.10 

11.25 

11.40 

11.55 

11.70 

11.85 

.80 

12.00 

12.15 

12.30 

12.45 

12.60 

12.75 

12.90 

13.05 

13.20 

13.35 

.90 

13.50 

13.65 

13.80 

13.95 

14.10 

14.25 

14.40 

14.55 

14.70 

14.85 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  17. — For  conversion  of  mean  time  into  sidereal  time. 


113 


.m 

0 

m 
1 

m 
2 

m 
3 

0 

h    m    s 
000 

h    m    s 
6     5     15 

h    m     s 
12    10    29 

h    m     s 
18    15    44 

1 
s           m      s 
0.00          00 

0.50 

m     s 
3      3 

1 

2 
3 
4 
5 
6 

B 
9 

06      5 
0    12    10 
0    18    16 
0    24    21 
0    30    26 
0    36    31 
0    42    37 
0    48    42 
0    54    47 

6    11    20 
6    17    25 
6    23    30 
6    29    36 
6    35    41 
6    41    46 
6    47    51 
6    53    56 
702 

12    16    34 
12    22    40 
12    28    45 
12    34    50 
12    40    55 
12    47      1 
12    53      6 
12    59    11 
13      5    16 

18    21    49 
18    27    54 
18    33    59 
18    40      5 
18    46    10 
18    52    15 
18    58    20 
19      4    26 
19    10    31 

0.01 
0.02 
0.03 
0.04 
0.05 
0.06 
0.07 
0.08 
0.09 

0         4 
0         7 
0  .     11 
0       15 
0        18 
0        22 
0        26 
0        29 
0        33 

0.51 
0.52 
0.53 
0.54 
0.55 
0.56 
0.57 
0.58 
0.59 

3      6 
3    10 
3    14 
3    17 
3    21 
3    25 
3    28 
3    32 
3    35 

10 

1      0    52 

767 

13    11    21 

19    16    36 

0.10 

0        37 

0.60' 

3    39 

11 
12 

13 
14 
15 
16 
17 
18 
19 

6    58 
13      3 
19      8 
25    13 
31    19 
37    24 
43    29 
1    49    34 
1    55    40 

7    12    12 
7    18    17 
7    24    23 
7    30    28 
7    36    33 
7    42    38 
7    48    44 
7    54    49 
8      0    54 

13    17    27 
13    23    32 
13    29    37 
13    35    42 
10    41    48 
13    47    53 
13    53    58 
14      0      3 
14      6      9 

19    22    41 
19    28    47 
19    34    52 
19    40    57 
19    47      2 
19    53      7 
19    59    13 
20      5    18 
20    11    23 

0.11 
0.12 
0.13 
0.14 
0.15 
0.16 
0.17 
0.18 
0.19 

0        40 
0       44 
0        47 
0       51 
0       55 
0        58 
1          2 
1          6 
1          9 

0.61 
0.62 
0.63 
0.64 
0.65 
0.66 
0.67 
0.68 
0.69 

3    43 
3    46 
3    50 
3    54 
3    57 
4      1 
4      5 
4      8 
4    12 

20 

2      1    45 

8      6    59 

14    12    14 

20    17    28 

0.20 

1        13 

0.70 

4    16 

21 
22 
23 
24 
25 
26 
27 
28 
29 

2      7    50 
2    13    55 
2    20      1 
2    26      6 
2    32    11 
2    38    16 
2    44    22 
2    50    27 
2    56    32 

8    13      5 
8    19    10 
8    25    15 
8    31    20 
8    37    26 
8    43    31 
8    49    36 
8    55    41 
9      1    47 

14    18    19 
14    24    24 
14    30    30 
14    36    35 
14    42    40 
14    48    45 
14    54    51 
15      0    56 
15      7      1 

20    23    34 
20    29    39 
20    35    44 
20    41    49 
20    47    55 
20    54      0 
21      0      5 
21      6    10 
21    12    16 

0.21 
0.22 
0.23 
0.24 
0.25 
0.26 
0.27 
0.28 
0.29 

1        17 
1        20 
1        24 
1        28 
1        31 
1        35 
1        39 
1        42 
1        46 

0.71 
0.72 
0.73 
0.74 
0.75 
0.76 
0.77 
0.78 
0.79 

4    19 
4    23 
4    27 
4    30 
4    34 
4    38 
4    41 
4    45 
4    49 

30 

3      2    37           9      7    52 

15    13      6 

21     18    21 

0.30 

1        50    , 

0.80 

4    52 

31 
32 
33 
34 
35 
36 
37 
38 
39 

3      8    43 
3    14    48 
3    20    53 
3    26    58 
3    33      3 
3    39      9 
3    45    14 
3    51    19 
3    57    24 

9    13    57 
9    20      2 
9    26      8 
9    32    13 
9    38    18 
9    44    23 
9    50    28 
9    56    34 
10      2    39 

15    19    12 
15    25    17 
15    31    22 
15    37    27 
15    43    33 
15    49    38 
15    55    43 
16      1    48 
16      7    54 

21    24    26 
21    30    31 
21    36    37 
21    42    42 
21    48    47 
21    54    52 
22      0    58 
22      7      3 
22    13      8 

0.31 
0.32 
0.33 
0.34 
0.35 
0.36 
0.37 
0.38 
0.39 

1        53 

1        57 
2          1 
2          4 
2          8 
2        11 
2        15 
2        19 
2        22 

0.81 
0.82 
0.83 
0.84 
0.85 
0.86 
0.87 
0.88 
0.89 

4    56 
4    59 
5      3 
5      7 
5    10 
5    14 
5    18 
5    21 
5    25 

40 

4      3    30 

10      8    44 

16    13    59 

22    19    13 

0.40 

2        26 

0.90 

5    29 

41 
42 
43 
44 
45 
46 
47 
48 
49 

4      9    35 
4    15    40 
4    21    45 
4    27    51 
4    33    56 
4    40      1 
4    46      6 
4    52    12 
4    58    17 

10    14    49 
10    20    55 
10    27      0 
10    33      5 
10    39    10 
10    45    16 
•10    51    21 
10    57    26 
11      3    31 

16    20      4 
16    26      9 
16    32    14 
16    38    20 
16    44    25 
16    50    30 
16    56    35 
17      2    41 
17      8    46 

22    25    19 
22    31    24 
22    37    29 
22    43    34 
22    49    39 
22    55    45 
23      1    50 
23      7    55 
23    14      0 

0.41 
0.42 
0.43 
0.44 
0.45 
0.46 
0.47 
0.48 
0.49 

2        30 
2        33 
2        37 
2        41 
2        44 
2        48 
2        52 
2        55 
2        59 

0.91 
0.92 
0.93 
0.94 
0.95 
0.96 
0.97 
0.98 
0.99 

5    32 
5    36 
5    40 
5    43 
5    47 
5    51 
5    54 
5    58 
6      2 

50 

5      4    22 

11      9    37 

17    14    51 

23    20      6 

o.:,o 

'3          3    |      1.00 

6      5 

51 
52 
53 
54 
55 
56 
57 
58 
59 

5    10    27 
5    16    33 
5    22    38 
5    28    43 
5    34    48 
5    40    54 
5    46    59 
5    53      4 
5    59      9 

11    15    42 
11    21    47 
11    27    52 
11    33    58 
11    40      3 
11    46      8 
11    52    13 
11    58    19 
12      4    24 

17    20    56 
17    27      2 
17    33      7 
17    39    12 
17    45    17 
17    51    23 
17    57    28 
18      3    33 
18      9    38 

23    26    11 
23    32    16 
23    38    21 
23    44    27 
23    50    32 
23    56    37 
24      2    42 
24      8    48 
24    14    53 

Example:  Let  the  given  mean 
time  be  14»»  57">  32  ».  56. 
The  table  gives 
nrstforl4'>54n>51»      2™  27" 
then  for         2    41.56         0.44 

2  27.44 
The  sum 
14"  57"  32  '.  56+2"°  27'.  44=15>>  0«>  0- 
is  the  required  sidereal  time. 

60 

6      5    15 

12    10    29 

18    15    44 

24    20    58 

46061—08- 


114  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  18. — For  conversion  of  sidereal  time  into  mean  time. 


s 

m 
0 

m 
1 

m 
2 

m 
3 

• 

0 

h    m     s 
000 

h    m    s 
6      6    15 

h    m     s 
12    12    29 

h     m     s 

18    18    44 

s 
0.00 

m     s 
0      0 

s 
0.50 

m     s 
3      3 

1 
2 
3 
4 
5 
6 
7 
8 
9 

066 
0    12    12 
0    18    19 
0    24    25 
0    30    31 
0    36    37 
0    42    44 
0    48    50 
0    54    56 

6    12    21 
6    18    27 
6    24    33 
6    30    40 
6    36    46 
6    42    52 
6    48    58 
6    55      4 
7      1    11 

12    18    35 
12    24    42 
12    30    48 
12    36    54 
12    43      0 
12    49      7 
12    55    13 
13      1    19 
13      7    25 

18    24    50 
18    30    56 
18    37      2 
18    43      9 
18    49    15 
18    55    21 
19      1    27 
19      7    34 
19    13    40 

0.01 

0.02 
0.03 
0.04 
0.05 
0.06 
0.07 
0.08 
0.09 

0      4 
0      7 
0    11 
0    15 
0    18 
0    22 
0    26 
0    29 
0    33 

0.51 
0.52 
0.53 
0.54 
0.55 
0.56 
0.57 
0.58 
0.59 

3      7 
3    10 
3    14 
3    18 
3    21 
3    25 
3    29 
3    32 
3    36 

10 

112 

7      7    17 

13    13    31 

19    19    46 

0.10 

0    37 

0.60 

3    40 

11 
12 
13 
14 
15 
16 
17 
18 
19 

7      9 
13    15 
19    21 
25    27 
31    34 
37    40 
43    46 
49    52 
55    59 

7    13    23 
7    19    29 
7    25    36 
7    31    42 
7    37    48 
7    43    54 
7    50      1 
7    56      7 
8      2    13 

13    19    38 
13    25    44 
13    31    50 
13    37    56 
13    44      3 
13    50      9 
13    56    15 
14      2    21 
14      8    28 

19    25    52 
19    31    59 
19    38      5 
19    44    11 
19    50    17 
19    56    23 
20      2    30 
20      8    36 
20    14    42 

0.11 
0.12 
0.13 
0.14 
0.15 
0.16 
0.17 
0.18 

0:19 

0    40 
0    44 
0    43 
0    51 
0    55 
0    59 
1      2 
1      6 
1    10 

0.61 
0.62 
0.63 
0.64 
0.65 
0.66 
0.67 
0.68 
0.69 

3    43 
3    47 
3    51 
3    54 
3    58 
4      2 
4      5 
4      9 
4    13 

20 

225 

8      8    19 

14    14    34 

20    20    48 

0.20 

1     13 

0.70 

4    16 

21 
22 
23 
24 
25 
26 
27 
28 
29 

2      8    11 
2    14    17 
2    20    24 
2    26    30 
2    32    36 
2    38    42 
2    44    49 
2    50    55 
2    57      1 

8    14    26 
8    20    32 
8    26    88 
8    32    44 
8    38    51 
8    44    57 
-     8    51      3 
8    57      9 
9      3    16 

14    20    40 
14    26    46 
14    32    53 
14    38    59 
14    45      5 
14    51    11 
14    57    18 
15      3    24 
15      9    30 

20    26    55 
20    33      1 
20    39      7 
20    45    13 
20    51    20 
20    57    26 
21      3    32 
21      9    38 
21    15    45 

0.21 
0.22 
0.23 
0.24 
0.25 
0.26 
0.27 
0.28 
0.29 

1    17 
1    21 
1    24 
1    28 
1    32 
1    35 
1    39 
1    43 
1    46 

0.71 
0.72 
0.73 
0.74 
0.75 
0.76 
0.77 
0.78 
0.79 

4    20 
4    24 
4    27 
4    31 
4    35 
4    38 
4    42 
4    46 
4    49 

30 

337 

9      9    22 

15    15    36 

21    21    51 

0.30 

1    50 

0.80 

4    53 

31 
32 
33 
34 
35 
36 
37 
38 
39 

3      9    14 
3    15    20 
3    21    26 
3    27    32 
3    33    38 
3    39    45 
3    45    51 
3    51    57 
3    58      3 

9    Ib    28 
9    21    34 
9    27    41 
9    33    47 
9    39    53 
9    45    59 
9    52      5 
9    58    12 
10      4    18 

15    21    43 
15    27    49 
15    33    55 
15    40      1 
15    46      8 
15    52    14 
15    58    20 
16      4    26 
16    10    33 

21    27    57 
21    34      3 
21    40    10 
21    46    16 
21    52    22 
21    58    28 
22      4    35 
22    10    41 
22    16    47 

0.31 
0.32 
0.33 
0.34 
0.35 
0.36 
0.37 
0.38 
0.39 

1    54 
1    57 
2      1 
2      5 
2      8 
2    12 
2    16 
2    19 
2    23 

0.81 
0.82 
0.83 
0.84 
0.85 
0.86 
0.87 
0.88 
0.89 

4    57 
5      0 
5      4 
5      8 
5    11 
5    15 
5    19 
5    22 
5    26 

40 

4      4    10 

10    10    24 

16    16    39 

22    22    53 

0.40 

2    26 

0.90 

5    30 

41 
42 
43 
44 
45 
46 
47 
48 
49 

4    10    16 
4    16    22 
4    22    28 
4    28    35 
4    34    41 
4    40    47 
4    46    53 
4    53      0 
4    59      6 

10    16    30 
10    22    37 
10    28    43 
10    34    49 
10    40    55 
10    47      2 
10    53      8 
10    59    14 
11      5    20 

16    22    45 
16    28    51 
16    34    57 
16    41      4 
16    47    10 
16    53    16 
16    59    22 
17      5    29 
17    11    35 

22    29      0 
22    35      6 
22    41    12 
22    47    18 
22    53    24 
22    59    31 
23      5    37 
23    11    43 
23    17    49 

0.41 

0.42 
0.43 
0.44 
0.45 
0.46 
0.47 
0.48 
0.49 

2    30 
2    34 
2    37 
2    41 
2    45 
2    48 
2    52 
2    56 
2    59 

0.91 
0.92 
0.93 
0.94 
0.95 
0.96 
0.97 
0.98 
0.99 

5    33 
5    37 
5    41 
5    44 
5    48 
5    52 
5    55 
5    59 
6      3 

50 

5      5    12 

11    11    27 

17    17    41 

23    23    56 

0.50 

30 
o 

1.00 

6      6 

51 
52 
53 
54 
55 
56 
57 
58 
59 

5    11    18 
5    17    25 
5    23    31 
5    29    37 
5    35    43 
6    41    50 
5    47    56 
5    54      2 
608 

11    17    33 
11    23    39 
11    29    45 
11    35    52 
11    41    58 
11    48      4 
11    54    10 
12      0    17 
12      6    23 

17    23    47 
17    29    54 
17    36      0 
17    42      6 
17    48    12 
17    54    19 
18      0    25 
18      6    31 
18    12    37 

23    30      2 
23    36      8 
23    42    14 
23    48    21 
23    54    27 
24      0    33 
24      6    39 
24    12    46 
24    18    52 

Example:  Given  15h  Om  0s. 
The  table  gives 
first  for    14*  57""  18"        2~27» 
then  for         2    42               0.44 

The 

15h()m 

15    0      0         2   27.44 
difference 
>  _  2m  278.44  =  14^  57-"  32".56 
required  mean  time. 

60 

6  '  6    15 

12    12    29 

18    18    44 

24    24    58 

is  the 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  19. — For  inlerconversion  of  feet  and  decimals  of  a  mile. 


115 


Feet.    Miles. 

Feet. 

Miles. 

Feet. 

Miles. 

Feet. 

Miles. 

53 

.01 

1373 

.26 

2693 

.51 

4013 

.76 

106 

.02 

1426 

.27 

2746 

.52 

4066 

.77 

158 

.03 

1478 

.28 

2798 

.53 

4118 

.78 

211 

.04 

1531 

.29 

2851 

.54 

4171 

.79 

264 

.05 

1584 

.30 

2904 

.55 

4224 

.80 

317 

.06 

1637 

.31 

2957 

.56 

4277 

.81 

370 

.07 

1690 

.32 

3010 

.57 

4330 

.82 

422 

.08 

1742 

.33 

3062 

.58 

4382 

.83 

475 

.09 

1795 

.34 

3115 

.59 

4435 

.84 

528 

.10 

1848 

.35 

3168 

.60 

4488 

.85 

581 

.11 

1901 

.36 

3221 

.61 

4541 

.86 

634 

.12 

1954 

.37 

3274 

.62 

4594 

.87 

686 

.13 

2006 

.38 

3326 

.63 

4646 

.88 

739 

.14 

2059 

.39 

3379 

.64 

4699 

.89 

792 

.15 

2112 

.40 

3432 

.65 

4752 

.90 

845 

.16 

2165 

.41 

3485 

.66 

4805 

.91 

898 

.17 

2218 

.42 

3538 

.67 

4858 

.92 

950 

.18 

2270 

.43 

3590 

.68 

4910 

.93 

1003 

.19 

2323 

.44 

3643 

.69 

4963 

.94 

1056 

.20 

2376 

.45 

3696 

.70 

5016 

.95 

1109 

.21 

2429 

.46 

3749 

.71 

5069 

.96 

1162 

.22 

2482 

.47 

3802 

.72 

5122 

.97 

1214 

.23 

2534 

.48 

3854 

.73 

5174 

.98 

1267 

.24 

2587 

.49 

3907 

.74 

5227 

.99 

1320 

.25 

2640 

.50 

3960 

.75 

5280 

1.00 

116 


GEOGBAPHIC    TABLES    AND    FOKMULAS. 


TABLE  20. — Converting  wheel  revolutions  into  hundredths  of  a  mile. 

[Prepared  .by  J.  H.  Jennings.] 
[Scale  divisions  outside;  revolutions  inside.] 
CIRCUMFERENCE  OF  WHEEL,  9.5  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

6 

11 

17 

22 

28 

33 

39 

44 

50 

56 

10 

61 

67 

72 

78 

83 

89 

94 

100 

105 

111 

20 

117 

122 

128 

133 

139 

144 

150 

155 

161 

167 

30 

172 

178 

183 

189 

194 

200 

205 

211 

216 

222 

40 

228 

233 

239 

244 

250 

255 

261 

266 

272 

278 

50 

283 

289 

294 

300 

305 

311 

316 

322 

328 

333 

60 

339 

344 

350 

355 

361 

366 

372 

378 

383 

389 

70 

394 

400 

405 

411 

416 

422 

428 

433 

439 

444 

80 

450 

455 

461 

466 

472 

478 

483 

489 

494 

500 

90 

506 

511 

516 

522 

528 

533 

539 

544 

550 

555 

CIRCUMFERENCE  OF  WHEEL,  9.6  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

11 

16 

22 

27 

33 

38 

44 

50 

55 

10 

60 

66 

72 

77 

82 

88 

93 

99 

105 

110 

20 

116 

121 

126 

132 

137 

143 

148 

154 

159 

165 

30 

171 

177 

182 

188 

193 

199 

204   209 

215 

220 

40 

225 

231 

236 

242 

247 

253 

258  !  264 

270 

275 

50 

281 

286 

292 

297 

303 

308 

314   319 

325 

330 

60 

336 

341 

347 

352 

358 

363 

369   374 

380 

385 

70 

391 

396 

402 

407 

413 

418 

424   429 

435 

440 

80 

446 

451 

457 

462 

468 

473 

479 

484 

490 

495 

90 

501 

506 

512 

517 

523 

528 

534 

539 

544 

550 

CIRCUMFERENCE  OF  WHEEL,  9.7  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

11 

16 

22 

27 

33 

38 

44 

49 

54 

10 

60 

65 

71 

76 

81 

87 

92 

98 

103 

109 

20 

114 

120 

125 

131 

136 

142 

147 

152 

158 

163 

30 

169 

174 

179 

185 

190 

196 

201 

206 

212 

218 

40 

223 

228 

234 

239 

245 

250 

256 

261 

267 

272 

50 

'"277 

283 

288 

294 

299 

305 

310 

316 

321 

326 

60 

331 

337 

342 

348 

353 

359 

364 

370 

376 

381 

70 

386 

392 

397 

403 

408 

414 

419 

424 

429 

435 

80 

441 

446 

451 

457 

462 

468 

473 

479 

484 

490 

90 

495 

500 

506 

511 

517 

522 

528 

533 

539 

544 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


117 


TABLE  20. — Converting  wheel  revolutions  into  hundredths  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  9.8  FEET. 


0 

1      2      3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

11 

16 

22 

27 

32 

38 

43 

49 

54 

10 

59 

65 

70 

75 

81 

86 

91 

97 

102 

108 

M 

113 

119 

124 

129 

135 

140 

145 

151 

156 

162 

30 

167 

172 

178 

183 

189 

194 

199 

205 

211 

216 

40 

221 

226 

231 

237 

242 

248 

253 

259 

265 

270 

50 

275 

280 

286 

291 

296 

302 

307 

313 

318 

324 

60 

329 

334 

339 

345 

350 

356 

361 

366 

372 

377 

70 

383 

388 

.394 

400 

405 

410. 

415 

421 

426 

431 

80 

437 

442 

447 

453 

458 

464 

469 

474 

480 

485 

*90 

490 

496 

501 

506 

512 

517 

522 

528 

533 

539 

CIRCUMFERENCE  OF  WHEEL,  9.9  FEET. 


0 

1 

2      3 

4 

5 

6 

7 

8      9 

10 

0 

6 

11 

16 

21 

27 

32 

37 

43 

48 

53 

10 

59 

64 

69 

75 

80 

85 

91 

96 

101 

107 

20 

112 

117 

122 

128 

133 

138 

144 

149 

155 

160 

30 

165 

170 

176 

181 

186 

192 

197 

203 

208 

213 

40 

219 

224 

229 

235 

240 

245 

251 

256 

261 

267 

50 

272 

277 

282 

288 

293 

298 

304 

309 

314 

320 

60 

325 

330 

336 

341 

346 

352 

357 

362 

368 

373 

70 

378 

384 

389 

394 

400 

405 

410 

416 

421 

426 

80 

432 

437 

442 

448 

453 

458 

464 

469 

474 

480 

90 

485 

490 

496 

501 

506 

512 

517 

522 

528 

533 

CIRCUMFERENCE  OF  WHEEL,  10  FEET. 


0 

1 

2      3 

4* 

5 

6 

7 

8 

9 

10 

0 

5 

11 

16 

21 

26 

32 

37 

42 

48 

53 

10 

58 

63 

69 

75 

80 

85 

90 

96 

101 

106 

20 

111 

116 

121 

127 

132 

137 

143 

148 

153 

158 

30 

164 

169 

174 

180 

185 

190 

195 

201 

206 

211 

40 

217 

222 

227 

232 

238 

243 

248 

253 

259 

264 

50 

269 

275 

280 

285 

290 

296 

301 

306 

311 

317 

60 

322 

327 

333 

338 

343 

349 

354 

359 

364 

370 

70 

375 

380 

385 

391 

396 

401 

406 

412 

417 

422 

80 

428 

433 

438 

444 

449 

454 

459 

465 

470 

475 

90 

481 

486 

491 

496 

502 

507 

512 

517 

523 

528 

118 


GEOGRAPHIC    TABLES    AND   FORMULAS. 


TABLE  20. — Converting  wheel  revolutions  into  hundredths  of  a  mile — Continued. 
CIRCUMFERENCE  OF  .WHEEL,  10.1  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

16 

21 

26 

31 

36 

41 

47 

52 

10 

58 

63 

68 

73 

79 

84 

89 

94 

100 

105 

20 

110 

115 

121 

126 

131 

136 

142 

147 

152 

157 

30 

162 

167 

173 

178 

183 

188 

193 

199 

204 

209 

40 

214 

220 

226 

231 

236 

241 

247 

252 

257 

262 

50 

267 

272 

277 

282 

288 

293 

298 

303 

308 

314 

60 

319 

324 

329 

334 

340 

345 

350 

355 

361 

366 

70 

371 

376 

381 

386 

392 

397 

402 

408 

413 

418 

80 

424 

429 

434 

439 

445 

450 

455 

460 

466 

471 

90 

476 

481 

486 

492 

497 

502 

507 

513 

518 

523 

CIRCUMFERENCE  OF  WHEEL,  10.2  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

16 

21 

26 

31 

36 

41 

47 

52 

10 

57 

62 

67 

73 

78 

83 

88 

93 

98 

104 

20 

109 

114 

119 

124 

130 

135 

140 

145 

150 

155 

30 

.  161 

166 

171 

176 

181 

186 

191 

197 

202 

207 

40 

212 

218 

224 

229 

234 

239 

244 

249 

254 

259 

50 

264 

269 

275 

280 

285 

290 

295 

300 

306 

311 

60 

316 

321 

326 

332 

337 

342 

347 

352 

357 

363 

70 

368 

373 

378 

383 

388 

394 

399 

404 

409 

414 

80 

419 

425 

430 

435 

440 

446 

451 

456 

461 

466 

90 

471 

476 

481 

487 

492 

497 

503 

508 

513 

518 

CIRCUMFERENCE  OF  WHEEL,  10.3  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

20 

26 

31 

36 

41 

46 

51 

10 

56 

62 

67 

72 

77 

82 

87 

92 

97 

103 

20 

108 

113 

118 

123 

128 

133 

138 

144 

149 

154 

30 

159 

164 

169 

174 

180 

185 

190 

195 

200 

204 

40 

209 

214 

219 

224 

230 

235 

240 

245 

250 

256 

50 

262 

267 

272 

277 

282 

287 

292 

297 

303 

308 

60 

313 

318 

323 

328 

333 

338 

344 

349 

354 

359 

70 

364 

369 

374 

380 

385 

390 

395 

400 

405 

410 

80 

416 

421 

426 

431 

436 

441 

446 

451 

457 

462 

90 

467 

472 

477 

482 

487 

492 

498 

503 

508 

513 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


119 


TABLE  20. — Converting  ivheel  revolutions  into  hundredths  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  10.4  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

20 

25 

30 

36 

41 

46 

51 

10 

56 

61 

66 

71 

76 

81 

86 

91 

97 

102 

20 

107 

112 

117 

122 

127 

132 

137 

142 

147 

152 

30 

157 

163 

168 

173 

178 

183 

188 

193 

198 

203 

40 

208 

213 

218 

223 

228 

233 

238 

244 

249 

254 

50 

259 

264 

269 

274 

279 

284 

289 

295 

300 

305 

60 

310 

315 

320 

325 

330 

335 

340 

345 

350 

356 

70 

361 

366 

371 

376 

k  381 

386 

391 

396 

401 

406 

80 

411 

416 

421 

426 

432 

437 

442 

447 

452 

457 

90 

462 

467 

472 

478 

483 

488 

493 

498 

503 

508 

1 

CIRCUMFERENCE  OF  WHEEL,  10.5  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

10 

55 

60 

65 

70 

75 

80 

85 

90 

95 

101 

20 

106 

111 

116 

121 

126 

131 

136 

141 

146 

151 

30 

156 

161 

166 

171 

176 

181 

186 

191 

196 

201 

40 

206 

211 

216 

221 

226 

231 

236 

241 

246 

251 

50 

257 

262 

267 

272 

277 

282 

287 

292 

297 

302 

60 

307 

312 

317 

322 

327 

332 

337 

342 

347 

352 

70 

357 

362 

367 

372 

377 

382 

387 

392 

397 

402 

80 

407 

.412 

417 

422 

428 

433 

438 

443 

448 

453 

90 

458 

463 

468 

473 

478 

483 

488 

493 

498 

503 

CIRCUMFERENCE  OF  WHEEL,  10.6  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

10 

55 

60 

65 

70 

75 

80 

85 

90 

95 

100 

20 

105 

110 

115 

120 

125 

130 

135 

140 

144 

149 

30 

154 

159 

164 

169 

174 

179 

184 

189 

194 

199 

40 

204 

209 

214 

219 

224 

229 

234 

239 

244 

249 

50 

254 

259 

264 

269 

274' 

279 

284 

289 

294 

299 

60 

304 

309 

314 

319 

324 

329 

334 

339 

344 

349 

70 

354 

359 

364 

369 

374 

379 

384 

389 

393 

398 

80 

403 

408 

413 

418 

423 

428 

433 

438 

443 

448 

90 

453 

458 

463 

468 

473 

478 

483 

488 

493 

498 

120 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  20. — Converting  wheel  revolutions  into  hundredth*  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  10.7  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

20 

25 

30 

35 

40 

44 

49 

10 

54 

59 

64 

69 

74 

79 

84 

89 

94 

99 

20 

104 

109 

114 

119 

123 

128 

133 

138 

143 

148 

30 

153 

158 

163 

168 

173 

178 

183 

188 

193 

198 

40 

203 

207 

212 

217 

222 

227 

232 

237 

242   247 

50 

252 

257 

262 

267 

272 

277 

282 

287 

291 

296 

60 

301 

306 

311 

316 

321 

326 

331 

336 

341 

346 

70 

351 

356 

361 

366 

371 

375 

380 

385 

390 

395 

80 

400 

405 

410 

415 

420 

425 

430 

435 

440 

.445 

90 

450 

454 

459 

464 

469 

474 

479 

484 

489 

494 

CIRCUMFERENCE  OF  WHEEL,  10.8  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

20 

24 

29 

34 

39 

44 

49 

10 

54 

59 

64 

68 

73 

78 

83 

88 

93 

98 

20 

103 

108 

113 

118 

122 

127 

132 

137 

142 

147 

30 

152 

156 

161 

166 

171 

176 

181 

186 

191 

196 

40 

200 

205 

210 

215 

220 

225 

230 

235  I  240 

244 

i 

50 

249 

254 

259 

264 

269 

274 

279 

283   288 

293 

60 

298 

303 

308 

313 

318 

323 

328 

332 

t337 

341 

70 

346 

351 

356 

361 

366 

371 

376 

381 

386 

391 

80 

396 

401 

406 

411 

416 

421 

425 

430 

435 

440 

90 

445 

450 

455 

460 

464 

469 

474 

479   484 

489 

CIRCUMFERENCE  OF  WHEEL,  10.9  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

15 

19 

24 

29 

34 

39 

44 

48 

10 

53 

58 

63 

68 

73 

78 

82 

87 

92 

97 

20 

102 

107 

111 

116 

121 

126 

131 

136 

141 

145 

30 

150 

155 

160 

165 

170 

175 

179 

184 

189 

193 

40 

197 

202 

207 

212 

217 

222 

227 

232 

237 

242 

50 

247 

252 

257 

261 

'266 

271 

276 

281 

286 

290 

60 

295 

300 

305 

310 

315 

319 

324 

329 

334 

339 

70 

344 

349 

353 

358 

363 

368 

373 

378 

383 

387 

80 

392 

397 

402 

407 

411 

416 

421 

426 

431 

436 

90 

440 

445 

450 

455 

460 

465 

469 

474 

479 

484 

GEOGRAPHIC    TABLES    AND    FORMULAS.  121 

TABLE  20. — Converting  wheel  revolutions  into  hundredths  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  11.0  FEET. 


0 

1 

.1 

1 

« 

5 

6 

7 

8 

9 

10 

0 

5 

10 

14 

19 

24 

29 

33 

38 

43 

48 

10 

53 

57 

62 

67 

72 

76 

81 

86 

91 

96 

•20 

101 

106 

110 

115 

119 

124 

129 

134 

139 

144 

30 

149 

154 

158 

163 

168 

173 

178 

182 

187 

192 

40 

197 

202 

206 

211 

216 

221 

225 

230 

235 

240 

50 

245 

250 

254 

259 

263 

268 

273 

278 

283 

288 

60 

293 

298 

302 

307 

312 

317 

321 

326 

331 

336 

70 

341 

346 

350 

355 

360 

365 

369 

374 

379 

384 

80 

389 

394 

398 

403 

408 

413 

417 

422 

427 

432 

90 

437 

442 

446 

451 

456 

461 

465 

470 

475 

480 

CIRCUMFERENCE  OF  WHEEL,  11.1  FEET. 


0 

1 

* 

8 

4 

5 

6 

7 

8 

9 

10 

0 

5 

10 

14 

19 

24 

29 

33 

38 

43 

48 

10 

52 

57 

62 

66 

71 

76 

81 

85 

90 

95 

20 

100 

104 

109 

114 

119 

124 

129 

133 

138 

143 

30 

147 

152 

157 

161 

166 

171 

176 

180 

185 

190 

40 

195 

200 

205 

209 

214 

219 

224 

229 

233 

238 

50 

243 

248 

252 

257 

262 

267 

271 

276 

281 

286 

60 

290 

295 

300 

305 

309 

314 

319 

324 

328 

333 

70 

338 

343 

347 

352 

357 

362 

367 

371 

376 

381 

80 

386 

390 

395 

400 

405 

409 

414 

419 

424 

428 

90 

433 

438 

443 

447 

452 

457 

462 

466 

471 

476 

CIRCUMFERENCE  OF  WHEEL,  11.2  FEET. 


0 

1 

g 

« 

5 

6 

7 

8 

9 

10 

0 

5 

9 

14 

19 

24 

28 

33 

38 

42 

47 

10 

52 

57 

62 

66 

71 

76 

80 

84 

89 

94 

20 

99 

104 

108 

113 

117 

122 

127 

132 

137 

141 

30 

146 

151 

155 

160 

165 

169 

174 

179 

184 

188 

40 

193 

198 

203 

207 

212 

217 

222 

226 

231 

236 

50 

240 

245 

250 

255 

259 

264 

269 

274 

278 

283 

60 

287 

292 

297 

302 

307 

312 

316 

321 

326 

330 

70 

334 

339 

344 

348 

353 

358 

363 

367 

372 

377 

80 

382 

386 

391 

396 

400 

405 

410 

415 

419 

424 

90 

429 

434 

438 

443 

447 

452 

456 

461 

466 

471 

122 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  20. — Converting  wheel  revolutions  into  hundredths  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  11.3  FEET. 


0 

1 

2 

3 

4 

0 

0 

7 

8 

9 

10 

0 

5 

9 

14 

19 

23 

28 

33 

37 

42 

47 

10 

51 

56 

61 

65 

70 

74 

79 

83 

88 

93 

20 

98 

103 

108 

112 

117 

122 

126 

131 

135 

140 

30 

145 

150 

154 

159 

164 

168 

173 

1Z8 

183 

187 

40 

191 

196 

200 

205 

210 

215 

220 

224 

229 

234 

50 

238 

243 

248 

252 

257 

261 

266 

271 

276 

280 

60 

285 

290 

294 

299 

304 

308 

313 

318 

322 

327 

70 

332 

336 

341 

346 

350 

355 

360 

364 

370 

374 

80 

378 

383 

387 

392 

397 

402 

406 

411 

416 

420 

90 

425 

430 

434 

439 

444 

448 

453 

458 

462 

467 

CIRCUMFERENCE  OF  WHEEL,  11.4  FEET. 


0     1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

9 

14 

18 

23 

28 

32 

37 

42 

46 

10 

50 

56 

60 

65 

69 

74 

79 

83 

88 

93 

20 

97 

102 

107 

111 

116 

120 

125 

129 

134 

139 

30 

143 

148 

152 

157 

162 

167 

171 

176 

180 

185 

40 

190 

195 

199 

204 

208 

213 

217 

222 

227 

231 

50 

236 

241 

245 

250 

255 

259 

264 

269 

273 

278 

60 

282 

287 

291 

296 

301 

306 

310 

315 

319 

324 

70 

329 

333 

338 

343 

347 

352 

357 

361 

366 

370 

80  - 

375 

380 

384 

389 

394 

398 

403 

407 

412 

417 

90 

421 

426 

431 

435 

440 

445 

449 

454 

458 

463 

CIRCUMFERENCE  OF  WHEEL,  11.5  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

9 

14 

18 

23 

28 

32 

37 

41 

46 

10 

50 

55 

59 

63 

68 

72 

77 

82 

87 

92 

20 

96 

101 

105 

110 

114 

119 

124 

128 

133 

138 

30 

142 

147 

151 

156 

161 

165 

170 

174 

179 

184 

40 

188 

193 

197 

202 

207 

211 

216 

220 

225 

229 

50 

234 

239 

243 

248 

252 

257 

262 

266 

271 

275 

60 

280 

285 

289 

294 

298 

303 

308 

312 

317 

321 

70 

326 

331 

335 

340 

344 

349 

353 

358 

363 

367 

80 

372 

377 

381 

386 

390 

395 

399 

404 

409 

413 

90 

418 

422 

427 

432 

436 

441 

445 

450 

454 

459 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


123 


TABLE  2Q.—  Comerling  wheel  revolutions  into  hundredths  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  11.6  FEET. 


0 

1 

2 

3 

4      5 

6 

7 

8 

9 

10 

0 

5 

9 

14 

18 

23 

27 

32 

36 

41 

46 

10 

50 

55 

59 

64 

68 

73 

77 

82 

87 

91 

20 

96 

100 

104 

109 

114 

118 

123 

127 

132 

136 

30 

141 

146 

150 

155 

159 

164 

168 

173 

178 

182 

40 

187 

191 

196 

200 

205 

209 

214 

218 

223 

227 

M 

232 

237 

241 

246 

250 

255 

259 

264 

269 

273 

60 

278 

282 

287 

291 

296 

300 

305 

309 

314 

318 

70 

323 

328 

332 

337 

341 

346 

350 

355 

360 

364 

80 

369 

373 

378 

382 

387 

391 

396 

400 

405 

410 

90 

414 

419 

423 

428 

432 

437 

441 

446 

450 

455 

CIRCUMFERENCE  OF  WHEEL,  11.7  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

5 

9 

13 

18 

23 

27 

32 

36 

41 

45 

10 

50 

54 

59 

63 

68 

72 

77 

81 

86 

90 

20 

95 

99 

104 

108' 

113 

117 

122 

126 

131 

135 

30 

140 

144 

149 

153 

158 

162 

167 

171 

176 

180 

40 

185 

189 

194 

198 

203 

207 

212 

217 

221 

225 

50 

230 

235 

239 

244 

248 

253 

257 

262 

266 

271 

60 

275 

280 

284 

289 

293 

298 

302 

307 

311 

316 

70 

320 

325 

329 

334 

338 

343' 

347 

352 

*356 

361 

80 

365 

370 

374 

379 

383 

388 

392 

397 

401 

406 

90 

410 

415 

419 

424 

428 

433 

437 

442 

446 

451 

CIRCUMFERENCE  OF  WHEEL,  11.8  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

4 

9 

13 

18 

22 

27 

32 

36 

40 

45 

10 

49 

53 

58 

62 

67 

72 

76 

80 

85 

89 

20 

94 

"98 

103 

107 

112 

116 

121 

125 

130 

134 

30 

139 

143 

148 

152 

157 

161 

165 

170 

174 

179 

40 

183 

187 

192 

197 

201 

206 

210 

215 

219 

223 

50 

228 

232 

237 

241 

246 

250 

255 

259 

264 

268 

60 

273 

277 

282 

286 

291 

295 

300 

304 

309 

313 

70 

317 

321 

326 

330 

335 

339 

344 

348 

353 

358 

80 

362 

367 

372 

376 

380 

385 

389 

393 

398 

402 

90 

407 

411 

416 

420 

425 

429 

434 

438 

443 

447 

124 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  20. — Converting  wheel  revolutions  into  hundredths  of  a  mile — Continued. 

CIRCUMFERENCE  OF  WHEEL,  11.9  FEET. 


0 

1 

2 

3 

4 

0 

6 

7 

8 

9      10 

0 

4 

9 

13 

18 

22 

27 

31 

'35 

40 

44 

10 

49 

53 

58 

62 

67 

71 

76 

80 

84 

89 

20 

93 

98 

102 

107 

111 

115 

120 

124 

129 

133 

30 

138 

142 

146 

151 

155 

160 

164 

169 

173 

178 

40 

182 

187 

191 

195 

200 

204 

209 

213 

218 

222 

50 

226 

231 

235 

240 

244 

249 

253 

258 

262 

266 

60 

271 

275 

280 

284 

289 

293 

298 

302 

306 

311 

70 

315 

320 

324 

329 

333 

338 

342 

346 

350 

355 

80 

360 

364 

369 

373 

377 

382 

386 

391 

395 

399 

90 

404 

409 

413 

417 

422 

426 

431 

435 

440 

444 

CIRCUMFERENCE  OF  WHEEL,  12  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

4 

9 

13 

18 

22 

26 

31 

35 

40 

44 

10 

48 

53 

57 

62 

66 

70 

75 

.  79 

84 

88 

20 

91 

96 

100 

104 

109 

'  113 

118 

122 

128 

132 

30 

136 

141 

145 

150 

154 

158 

163 

168   172 

176 

40 

180 

185 

189 

194 

198 

202 

207 

211  ;  216 

220 

50 

224 

229 

233 

238 

242 

246 

251 

255   260 

264 

60 

268 

273 

277 

281 

286 

290 

295 

299   304 

308 

70 

312 

317 

321 

326 

330 

334 

339 

343 

348 

352 

80 

356 

361 

365 

370 

374 

378 

383 

388 

392 

396 

90 

400 

405 

409 

414 

418 

422 

427 

431 

436 

440 

CIRCUMFERENCE  OF  WHEEL,  12.1  FEET. 


0 

1 

2 

3 

4 

5 

6 

7 

8      9 

10 

0 

4 

9 

13 

17 

22 

26 

31 

35 

39 

44 

10 

48 

53 

57 

61 

66 

70 

75 

79 

83 

87 

20 

91 

96 

100 

105 

109 

113 

118 

122 

126 

131 

30 

135 

139 

144 

148 

153 

157 

161 

165 

170 

174 

40 

178 

183 

187 

192 

196 

201 

205 

209 

214 

218 

50 

222 

227 

231 

235 

240 

244 

249 

253 

257 

262 

60 

266 

270 

275 

279 

283 

288 

292 

296 

301 

305 

70 

310 

314 

318 

323 

327 

331 

336 

340 

344 

349 

80 

353 

358 

362 

366 

370 

375 

379 

384 

388 

392 

90 

397 

401 

405 

410 

414 

419 

423 

427 

432 

436 

GEOGRAPHIC  TABLES  AND  FORMULAS. 


125 


TABLE  20. — Converting  wheel  revolutions  into  hundredth*  of  a  mile — Continued. 
CIRCUMFERENCE  OF  WHEEL,  12.2  FEET. 


0 

i  |  « 

3 

4 

5 

6 

7 

8 

9 

10 

0 

4 

9 

13 

17 

22 

26 

30 

35 

39 

43 

10 

48 

52 

56 

61 

65    69    74 

78 

82 

87 

20 

91 

95 

100 

104 

108   113   117 

121 

126 

130 

30 

134 

138 

143 

147 

151   156   160 

165 

169 

173 

40 

ITS 

182 

186 

191 

195   199   204 

208 

212 

.216 

50 

221 

225 

230 

234 

238   243   247 

251 

256 

260 

60 

264 

268 

273 

277 

281   286 

290 

294 

299 

303 

70 

307   312 

316 

320 

325   329 

333 

338 

342 

346 

80 

351 

356 

359 

364 

368 

372 

377 

381 

385 

390 

1*0 

395 

399 

404 

408 

412 

417 

421 

425 

429 

433 

After  measuring  wheel  use  nearest  tenth  for  size  of  wheel. 


126 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


TABLE  21. — Five-place  logarithms  of  natural  numbers, 

[Fractional  change  in  a  number  corresponding  to  a  change  in  its  logarithm.] 

Computed  from  the  formula, 


N  '         fi 
//=modulus  of  common  logarithms  =  0.43429448. 


For 

A  log  N 
=  1  unit  in 

A^ 
N 

For 
A  log  N 
=  4  units  in 

A.ZV 

IT 
(in  round 
numbers) 

Fourth  place 

rA* 

, 

Fifth  place 

Fifth  place  

Sixth  place 

Sixth  place  

Seventh  place     .   . 

Seventh  place  

GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


127 


N. 

L.  0      1      2      3      4 

56789 

0 

00  000  30  103  47  712  60  206 

69  897  77  815  84  510  90  309  95  424 

1 
2 
3 

4 
5 

6 

7 
8 
9 

00  000  04  139  07  918  11  394  14  613 
30  103  32  222  34  242  36  173  38  021 
47  712  49  136  50  515  51  851  53  148 

60  206  61  278  62  325  63  347  64  345 
69  897  70  757  71  600  72  428  73  239 
77  815  78  533  79  239  79  934  80  618 

84  510  85  126  85  733  86  332  86  923 
90  309  90  849  91  381  91  908  92  428 
95  424  95  904  96  379  %  848  97  313 

17  609  20  412  23  045  25  527  27  875 
39  794  41  497  43  136  44  716  46  240 
54  407  55  630  56  820  57  978  59  106 

65  321  66  276  67  210  68  124  69  020 
74  036  74  819  75  587  76  343  77  085 
81  291  81  954  82  607  83  251  83  885 

87  506  88  081  88  649  89  209  89  763 
92  942  93  450  93  952  94  448  94  939 
97  772  98  227  98  677  99  123  99  564 

10 

00  000  00  432  00  860  01  284  01  703 

02  119  02  531  02  938  03  342  03  743 

11 
12 
13 

14 
15 
16 

17' 
18 
19 

04  139  04  532  04  922  05  308  05  690 
07  918  08  279  08  636  08  991  09  342 
11  394  11  727  12  057  12  385  12  710 

14  613  14  922  15  229  15  534  15  836 
17  609  17  898  18  184  18  469  18  752 
20  412  20  683  20  952  21  219  21  484 

23  045  23  300  23  553  23  805  24  055 
25  527  25  768  26  007  26  245  26  482 
27  875  28  103  28  330  28  556  28  780 

06070  06446  06819  07188  07555 
09  691  10  037  10  380  10  721  11  059 
13  033  13  354  13  672  13  988  14  301 

16  137  16  435  16  732  17  026  17  319 
19  033  19  312  19  590  19  866  20  140 
21  748  22  Oil  22  272  22  531  22  789 

24  304  24  551  24  797  25  042  25  285 
26  717  26  951  27  184  27  416  27  646 
29  003  29  226  29  447  29  667  29  885  ' 

20 

30  103  30  320  30  535  30  750  30  963 

31  175  31  387  31  597  31  806  32  015 

21 
22 
23 

24 
25 
26 

27 
28 
29 

32  222  32  428  32  634  32  838  33  041 
34  242  34  439  34  635  34  830  35  025 
36  173  36  361  36  549  36  736  36  922 

38  021  38  202  38  382  38  561  38  739 
39  794  39  967  40  140  40  312  40  483 
41  497  41  664  41  830  41  9%  42  160 

43  136  43  297  43  457  43  616  43  775 
44  716  44  871  45  025  45  179  45  332 
46  240  46  389  46  538  46  687  46  835 

33  244  33  445  33  646  33  846  34  044 
35  218  35  411  35  603  35  793  35  984 
37  107  37  291  37  475  37  658  37  840 

38  917  39  094  39  270  39  445  39  620 
40  654  40  824  40  993  41  162  41  330 
42  325  42  488  42  651  42  813  42  975 

43  933  44  091  44  248  44  404  44  560 
45  484  45  637  45  788  45  939  46  090 
46  982  47  129  47  276  47  422  47  567 

30 

47  712  47  857  48  001  48  144  48  287 

48  430  48  572  48  714  48  855  48  996 

31 
32 
33 

34 
35 
36 

37 
38 
39 

49  136  49  276  49  415  49  554  49  693 
50  515  50  651  50  786  50  920  51  055 
51  851  51  983  52  114  52  244  52  375 

53  148  53  275  53  403  53  529  53  656 
54  407  54  531  54  654  54  777  54  900 
55  630  55  751  55  871  55  991  56  110 

56  820.  56  937  57  054  67  171  57  287 
57  978  58  092  58  206  58  320  58  433 
59  106  59  218  59  329  59  439  59  550 

49  831  49  969  50  106  50  243  50  379 
51  188  51  322  51  455  51  587  51  720 
52  504  52  634  52  763  52  892  53  020 

53  782  53  908  64  033  54  158  54  283 
55  023  55  145  55  267  55  388  55  509 
56  229  56  348  66  467  56  585  56  703 

57  403  57  519  57  634  57  749  57  864 
58  546  68  659  58  771  58  883  58  995 
59  660  69  770  59  879  59  988  60  097 

40 

60  206  60  314  60  423  60  531  60  638 

60  745  60  853  60  959  61  066  61  172 

41 
42 
43 

44 
45 
46 

47 
48 
49 

61  278  61  384  61  490  61  595  61  700 
62  325  62  428  62  531  62  634  62  737 
63  347  63  448  63  548  63  649  63  749 

64  345  64  444  64  542  64  640  64  738 
65  321  65  418  65  514  65  610  65  706 
66  276  66  370  66  464  66  558  66  652 

67  210  67  302  67  394  67  486  67  578 
68  124  68  215  68  305  68  395  68  485 
69  020  69  108  69  197  69  285  69  373 

61  805  61  909  62  014  62  118  62  221 
62  839  62  941  63  043  63  144  63  246 
63  849  63  949  64  048  64  147  64  246 

64  836  64  933  65  031  65  128  65  225 
65  801  65  896  65  992  66  087  66  181 
66  745  66  839  66  932  67  025  67  117 

67  669  67  761  67  852  67  943  68  034 
68  574  68  664  68  753  68  842  68  931 
69  461  69  548  69  636  69  723  69  810 

50 

69  897  69  984  70  070  70  157  70  243 

70  329  70  415  70  501  70  586  70  672 

N. 

L.  0      1      2      3      4 

56789 

0°  1'  = 

0   2  : 

0  3  = 
0  4  = 

=  60"   S.  4.  68  557   T.  4.  68  557    0 
=  120     4.  68  557     4.  68  557    0 
=  180     4.  68  557     4.  68  557    0 
=  240     4.68557     4.68558-   0 

0  5'  =  300"  S.  4.  68  557  T.  4.  68  558 
6  =  360     4.  68  557     4.  68  558 
7  =  420     4.  68  557    4.  68  568 
8  =  480     4.  68  657     4.  68  558 

128  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0  1  2  3  4 

56789 

50 

51 
52 
53 

54 
55 
56 

57 
58 
59 

60 

61 
62 
63 

64 

65 
66 

67 
68 
69 

70 

71 
72 
73 

74 
75 
76 

77 
78 
79 

80 

81 

82 
83 

84 
85 
86 

87 
88 
89 

90 

91 
92 
93 

94 
95 
96 

97 
98 
99 

100 

69  897  69  984  70  070  70  157  70  243 

70  329  70*  415  70  501  70  586  70  672 

70  757  70  842  70  927  71  012  71  096 
71  600  71  684  71  767  71  850  71  933 
72  428  72  509  72  591  72  673  72  754 

73  239  73  320  73  400  73  480  73  560 
74  036  74  115  74  194  74  273  74  351 
74  819  74  896  74  974  75  051  75  128 

75  587  75  664  75  740  75  815  75  891 
76  343  76  418  76  492  76  567  76  641 
77085  77159  77232  77305  77379 

71  181  71  265  71  349  71  433  71  517 
72  016  72  099  72  181  72  263  72  346 
72  835  72  916  72  997  73  078  73  159 

73  640  73  719  73  799  73  878  73  957 
74  429  74  507  74  586  74  663  74  741 
75  205  75  282  75  358  75  435  75  511 

75  967  76  042  76  118  76  193  76  268 
76  716  76  790  76  864  76  938  77  012 
77  452  77  525  77  597  77  670  77  743 

77  815  77  887  77  960  78  032  78  104 

78  176  78  247  78  319  78  390  78  462 

78  533  78  604  78  675  78  746  78  817 
79  239  79  309  79  379  79  449  79  518 
79  934  80  003  80  072  80  140  80  209 

80  618  80  686  80  754  80  821  80  889 
81  291  81  358  81  425  81  491  81  558 
81  954  82  020  82  086  82  151  82  217 

82  607  82  672  82  737  82  802  82  866 
83  251  83  315  83  378  83  442  83  506 
83  885  83  948  84  Oil  84  073  84  136 

78  888  78  958  79  029  79  099  79  169 
79  588  79  657  79  727  79  7%  79  865 
80  277  80  346  80  414  80  482  80  550 

80  956  81  023  81  090  81  158  81  224 
81  624  81  690  81  757  81  823  81  889 
82  282  82  347  82  413  82  478  82  543 

82  930  82  995  83  059  83  123  83  187 
83  569  83  632  83  69*5  83  759  83  822 
84  198  84  261  84  323  84  386  84  448 

84  510  84  572  84  634  84  696  84  757 

84  819  84  880  84  942  85  003  85  065 

85  126  85  187  85  248  85  309  85  370 
85  733  85  794  85  854  85  914  85  97,4 
86  332  86  392  86  451  86  510  86  570 

86  923  86  982  87  040  87  099  87  157 
87  506  87  664  87  622  87  679  87  737 
88  081  88  138  88  195  88  252  88  309 

88  649  88  705  88  762  88  818  88  874 
89  209  89  265  89  321  89  376  89  432 
89  763  89  818  89  873  89  927  89  982 

85  431  85  491  85  552  85  612  85  673 
86  034  86  094  86  153  86  213  86  273 
86  629  86  688  86  747  86  806  86  864 

87  216  87  274  87  332  87  390  87  448 
87  795  87  852  87  910  87  967.  88  024 
88  366  88  423  88  480  88  536  88  593 

88  930  88  986  89  042  89  098  89  154 
89  487  89  542  89  597  89  653  89  708 
90  037  90  091  90  146  90  200  90  255 

90  309  90  363  90  417  90  472  90  526 

90  580  90  634  90  687  90  741  90  795 

90  849  90  902  90  956  91  009  91  062 
91  381  91  434  91  487  91  540  91  593 
91  908  91  960  92  012  92  065  92  117 

92  428  92  480  92  531  92  583  92  634 
92  942  92  993  93  044  93  095  93  146 
93  450  93  500  93  551  93  601  93  651 

93  952  94  002  94  052  94  101  94  151 
94  448  94  498  94  547  94  59§  94  645 
94  939  94  988  95  036  95  085  95  134 

91  116  91  169  91  222  91  275  91  328 
91  645  91  698  91  751  91  803  91  855 
92  169  92  221  92  273  92  324  92  376 

92  686  92  737  92  788  92  840  92  891 
93  197  93  247  93  298  93  349  93  399 
93  702  93  752  93  802  93  852  93  902 

94  201  94  250  94  300  94  349  94  399 
94  694  94  743  94  792  94  841  94  890 
95  182  95  231  95  279  95  328  95  376 

95  424  95  472  95  521  95  569  95  617 

95  665  95  713  95  761  95  809  95  856 

95  904  95  952  95  999  96  047  96  095 
96  379  96  426  96  473  96  520  96  567 
96  848  96  895  96  942  96  988  97  035 

97  313  97  359  97  405  97  451  97  497 
97  772  97  818  97  864  97  909  97  955 
98  227  98  272  98  318  98  363  98  408 

98  677  98  722  98  767  98  811  98  856 
99  123  99  167  99  211  99  255  99  300 
99  564  99  607  99  651  99  695  99  739 

96  142  96  190  96  237  96  284  96  332 
96  614  96  661  96  708  96  755  96  802 
97  081  97  128  97  174  97  220  97  267 

97  543  97  589  97  635  97  681  97  727 
98  000  98  046  98  091  98  137  98  182 
98  453  98  498  _  98  543  98  588  98  632 

98  900  98  945  98  989  99  034  99  078 
99  344  99  388  99  432  99  476  99  520 
99  782  99  826  99  870  99  913  99  957 

00  000  00  043  00  087  00  130  00  173 

00  217  00  260  00  303  00  346  00  389 

v. 

L.  0  1  2  3  4 

56789 

0°  9'  =  540"  S.  4.  68  557  T.  4.  68  558    0°  13'  =  780"  S.  4.  68  557  T.  4.  68  558 
0  10  =  600     4.  68  557     4.  68  558    0  14  -=  840     4.  68  557    4.  68  558 
0  11  =  660     4.  68  557    4.  68  558    0  15  =  900     4.  68  557    4.  68  558 
0  12  =  720     4.  68  557    4.  68  558    0  16  =  960     4.  68  557    4.  68  558 

GEOGRAPHIC  .TABLES    AND    FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


129 


N. 

L.  0   1   2   3   4 

56789 

P.  P. 

100 

00  000  043  087  130  173 

217  260  303  346  389 

101 

432  475  518  56±  604 

647  689  732  775  817 

44   43   42 

102 
103 

860  903  945  988  *030 
01  284  326  368  410  452 

*072  *115  #157  *199  *242 
494  536  578  620  662 

1 
2 

4,4   4,3   4,2 

8,8   8,6   8,4 

104 

105 
106 

70S  745  787  828  870 
02  119  160  202  243  284 
531  572  612  653  694 

912  953  995  *036  #078 
325  366  407  449  490 
735  776  816  857  898 

3 
4 

5 
6 

13,2  12,9  12,6 
17,6  17,2  16,8 
22,0  21,5  21,0 
26,4  25,8  25,2 

107 
108 
109 

938  979  *019  *060  *100 
03  342  383  423  463  503 
743  782  822  862  902 

*14l  *181  *222  *262  *302 
543  583  623  663  703 
941  981  #021  *060  *100 

7 

8 
9 

30,8  30,1  29,4 
35,2  34,4  33,6 
39,6  38,7  37,8 

110 

04  139  179  218  258  297 

336  376  415  454  493 

111 
112 
113 

532  571  610  650  689 
922  961  999  *038  #077 
05  308  346  385  423  461 

727  766  805  844  883 
#115  #154  *192  #231  *269 
500  538  576  614  652 

1 
2 

41   40   39 

4,1   4,0   3,9 
8,2   8,0   7,8 

114 
115 
116 

690  729  767  805  843 
06  070  108  145  183  221 
446  483  521  558  595 

881  918  956  994  *032 
258  2%  333  371  408 
633  670  707  744  781 

3 
4 
5 
6 

12,3  12,0  11,7 
16,4  16,0  15,6 
20,5  20,0  19,5 
24,6  24,0  23,4 

117 
118 

819  856  893  930  967 
07  188  225  262  298  335 

*004  #041  *078  *115  #151 
372  408  445  482  518 

7 
8 
9 

28,7  28,0  27,3 
32,8  32,0  31,2 
36  9  36  0  35  1 

119 

556  591  628  664  700 

737  773  809  846  882 

120 

918  954  990  *027  *063 

,099  *135  *171  *207  #243 

121 

08  279  314  350  386  422 

458  493  529  565  600 

38   37   36 

122 

636  672  707  743  778 

814  849  884  920  955 

1 

38   37   36 

123 

991  *026  *061  *096  *132 

*167  *202  *237  *272  *307 

2 

7,6   7,4   7,2 

3 

Ily4    11  1    10  8 

124 
125 
126 

09  342  377  412  447  482 
691  726  760  795  830 
10  037  072  106  140  175 

517  552  587  621  656 
864  899  934  968  *003 
209  243  278  312  346 

4 
5 
6 

15,2  14,8  14,4 
19,0  .18,5  18,0 
22,8  22,2  21,6 

127 
'  128 
129 

380  415  449  483  517 
721  756  789  823  857 
11  059  093  126  160  193 

551  685  619  653  687 
890  924  958  992  *025 
227  261  294  327  361 

7 
8 
9 

26,6  25,9  25,2 
30,4  29,6  28,8 
34,2  33,3  32,4 

130 

394  428  461  494  528 

661  594  628  661  694 

131 

727  760  793  826  860 

893  926  959  992  *024 

35   34   33 

132 
133 

12  057  090  123  156  189 
385  418  450  483  516 

222  254  287  320  352 
548  581  613  646  678 

1 
2 

3,5   3,4   3,3 
7,0   6,8   6,6 

134 
135 
136 

710  743  775  808  840 
13  033  066  098  130  162 
354  386  418  450  481 

872  905  937  969  *001 
194  226  258  290  322 
513  545  577  609  640 

3 
4 
5 
6 

10,5  10,2   9,9 
14,0  13,6  13,2 
17,5  17,0  16,5 
21,0  20,4  19,8 

137 
138 

672  704  735  767  799 
988  *019  *051  *082  #114 

830  862  893  925  956 
*145  *176  *208  *239  #270 

7 
8 
9 

24,5  23,8  23,1 
28,0  27,2  26,4 
31,5  30  6  29  7 

139 

14  301  333  364  395  426 

457  489  520  551  582 

140 

613  644  675  706  737 

768  799  829  860  891 

141 

922  953  983  *014  #045 

#076  *106  *137  *168  *198 

32   31   30 

142 
143 

15  229  259  290  320  351 
534  564  594  625  655 

381  412  442  473  503 
685  715  746  776  806 

1 
2 

3,2   3,1   3,0 

6,4   6,2   6,0 

3 

9,6   9  3   9,0 

144 
145 
146 

836  866  897  927  957 
16  137  167  197  227  256 
435  465  495  524  554 

987  *017  *047  *077  #107 
286  316  346  376  406 
584  613  643  673  702 

4 
5 
6 

12,8  12,4  12,0 
16,0  15,5  15,0 
19,2  18,6  18,0 

147 
148 
149 

732  761  791  820  850 
17  026  056  085  114  143 
319  348  377  406  435 

879  909  938  967  997 
173  202  231  260  289 
464  493  522  551  580 

7 
8 
9 

22,4  21,7  21,0 
25,6  24,8  24,0 
28,8  27,9  27,0 

150 

609  638  667  696  725 

754  782  811  840  869 

X. 

L.  0   1   2   3   4 

56789 

P.  P. 

0°  16'  =  960"  S.  4.  68  557  T.  4.  68  558    0°  21'  =  1260"  S.  4.  68  557  T.  .  68  558 

0  17  =  1020    4.  68  557    4.  68  558    0  22  =  1320    4.  68  557    4.  68  558 

0  18  =  1080    4.  68  557    4.  68  558    0  23  =  1380    4.  68  557     .  68  558 

0  19  =  1140    4.  68  557    4.  68  558    0  24  =  1440    4.  68  557    <  .  68  558 

0  20  =  1200    4.  68  557    4.  68  558    0  25  =  1500    4.  68  557     .68  558 

46061—08 9 


130  GEOGEAPHIC    TABLES    AND    FOEMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

56789 

P.  P. 

150 

17  609  638  667  696  725 

754  782  811  840  869 

151 
152 

898  926  955  984  *013 
18  184  213  241  270  298 

*041  *070  *099  *127  *156 
327  355  384  412  441 

29    28 

163 

469  498  526  554  583 

611  639  667  696  724 

1 

2,9   2,8 

2 

5,8   5,6 

154 

752  780  808  837  865 

893  921  949  977  *005 

3 

8,7   8,4 

155 

19  033  061  089  117  145 

173  201  229  257  285 

4 

11,6   11,2 

156 

312  340  368  396  424 

451  479  507  535  562 

5 

14,5  14,0 

6 

17,4  16,8 

157 

590  618  645  673  700 

728  756  783  811  838 

7 

20,3  19,6 

158 

866  893  921  948  976 

*003  *030  #058  *085  *112 

8 

23,2  22,4 

159 

20  140  167  194  222  249 

276  303  330  358  385 

9 

26,1  25,2 

160 

412  439  466  493  520 

548  575  602  629  656 

161 

683  710  737  763  790 

817  844  871  898  925 

O7     .)<: 

162 
163 

952  978  *005  *032  #059 
21  219  245  272  299  325 

*085  *112  *139  *165  *192 
352  378  405  431  458 

1 

—  0       -  »  » 

2,7   2,6 

2 

6,4   5,2 

164 

484  511  537  564  590 

617  643  669  696  722 

3 

8,1   7,8 

165 

748  775  801  827  854 

880  906  932  958  985 

4 

10,8  10,4 

166 

22  Oil  037  063  089  115 

141  167  194  220  246 

5 

13,5  13,0 

6 

16,2  15,6 

167 

272  298  324  350  376 

401  427  453  479  505 

7 

18,9  18,2 

168 

531  557  583  608  634 

660  686  712  737  763 

8 

21,6   20,8 

169 

789  814  840  866  891 

917  943  968  994  *019 

9 

24,3  23,4 

170 

23  045  07C  096  121  147 

172  198  223  249  274 

171 

300  325  350  376  401 

426  452  477  502  528 

172 
173 

553  578  603  629  654 
805  830  855  880  905 

679  704  729  754  779 
930  955  980  *005  *030 

1   2,6 

2   5,0 

174 

24  055  080  105  130  155 

180  204  229  254  279 

3   7,5 

175 

304  329  353  378  403 

428  452  477  502  527 

4  10,0 

176 

551  576  601  625  650 

674  699  724  748  773 

5  12,5 

6  15,0 

177 
178 

797  822  846  871  895 
25  042  066  091  115  139 

920  944  969  993  *018 
164  188  212  237  261 

7  17,5 
8  20,0 

179 

285  310  334  358  382 

406  431  455  479  503 

9  22,5 

180 

627  551  575  600  624 

648  672  696  720  744 

181 
182 
183 

768  792  816  840  864 
26  007  031  055  079  102 
245  269  293  316  340 

888  912  935  959  983 
126  150  174  198  221 
364  387  411  435  458 

1 

24   23 

2,4   2,3 

2 

4,8   4,6 

184 

482  505  529  553  576 

600  623  647  670  694 

3 

7,2   6,9 

185 
186 

717  741  764  788  811 
951  975  998  *021  *045 

834  858  881  905  928 
*068  *091  #114  #138  *161 

4 
5 

9,6   9,2 
12,0  11,5 

6 

14,4  13,8 

187 

27  184  207  231  254  277 

300  323  346  370  393 

7 

16,8  16,1 

188 

416  439  462  485  508 

531  554  577  600  623 

8 

19,2  18,4 

189 

646  669  692  715  738 

761  784  807  830  852 

9 

21,6  20,7 

190 

875  898  921  944  967 

989  #012  #035  *058  *081 

191 

28  103  126  149  171  194 

217  240  262  285  307 

22   21 

192 

330  353  375  398  421 

443  466  488  511  533 

193 

556  578  601  623  646 

668  691  713  735  758 

1 

2,2   2,1 

2 

4,4   4,2 

194 

780  803  825  847  870 

892  914  937  959  981 

3 

6,6   6,3 

195 

29  003  026  048  070  092 

115  137  159  181  203 

4 

8,8   8,4 

196 

226  248  270  292  314 

336  358  380  403  425 

5 

11,0  10,5 

6 

13,2  12,6 

197 

447  469  491  513  535 

557  579  601  623  645 

7 

15,4  14,7 

198 

667  688  710  732  754 

776  798  820  842  863 

8 

17,6  16,8 

199 

885  907  929  951  973 

994  *016  *038  *060  *081 

9 

19,8  18,9 

200 

30  103  125  146  168  190 

211  233  255  276  298 

'  N. 

L.  0   1   2   3   4 

56789 

P.  P. 

0°  25'  =  1500"  S.  4.  68  657  T.  4.  68  558    0°  30'  =  1800"  S.  4.  68  557  T.  4.  68  559 

0  26  =  1560    4.  68-  557    4.  68  558     0  31  =  1860    4.  68  557    4.  68  559 

0  27  =  1620    4.  68  557    4.  68  558     0  32  =  1920    4.  68  557    4.  68  559 

0  28  =  1680    4.  68  557    4.  68  558     0  33  =  1980    4.  68  557    4.  68  559 

0  29  -  1740    4.  68  557    4.  68  558    0  34  =  2040    4.  68  557    4.  68  669 

GEOGRAPHIC   TABLES    AND    FORMULAS. 
TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


131 


N. 

L.  0   1   2   3   4 

5 

6789 

P.  P. 

200 

30  103  125  146  168  190 

211  233  255  276  298 

201 

329  341  363  384  406 

428  449  471  492  514 

22    21 

202 

535  557  578  600  621 

643 

664  685  707  728 

1   22   21 

203 

7jk)  771  792  814  835 

856 

878  899  920  942 

2   4^4   4,2 

3   66   63 

204 

205 

963  984  #006  *027  *048 
31  175  197  218  239  260 

*069  *091  *112  #133  #154 
281  302  323  34§  366 

4   8,8   8,4 
5  11,0  10,5 

206 

387  408  429  450  471 

492 

513  534  555  676 

6  13,2  12,6 

207 
208 
209 

597  618  639  660  681 
806  827  848  869  890 
32  015  035  056  077  098 

702  723  744  765  785 
911  931  952  973  994 
118  139  160  181  201 

7  15,4  14,7 
8  17,6  16,8 
9  19,8  18,9 

210 

222  243  263  284  305 

325  346  366  387  408 

211 

428  449  469  490  519 

531  562  572  593  613 

20 

212 

634  654  675  695  715 

736 

756  777  797  818 

1    on 

213 

838  858  879  899  919 

940 

960  980  #001  #021 

JL 

2 

i*f\J 

4,0 

214 

215 

33  041  062  082  102  122 
244  264  284  304  325 

18 

163  183  20?  224 
365  385  405  425 

3 

4 
5 

6,0 
8,0 
10,0 

216 

445  465  486  506  526 

646 

566  586  606  626 

6 

12,0 

217 
218 

646  666  686  706  726 
846  866  885  905  925 

746 
945 

766  786  806  826 
965  985  *005  #025 

7 
8 
g 

14,0 
16,0 
ifl  n 

219 

34  044  064  084  104  124 

143 

163  183  203  223 

220 

242  262  282  301  321 

341 

361  380  400  420 

221 

439  459  479  498  518 

537 

557  577  596  616 

19 

222 

635  655  674  694  713 

733 

753  772  792  811 

1   1  Q 

223 

830  850  869  889  908 

928 

947  967  986  #005 

2 

3,8 

224 
225 

35  025  044  064  083  102 
218  238  257  276  295 

315 

141  160  180  199 
334  353  372  392 

3 
4 
5 

5,7 
7,6 
9  5 

226 

411  430  449  468  488 

607 

526  545  564  583 

6 

«J,tF 

11/4 

227 
228 

603  622  641  660  679 
793  813  832  851  870 

698 
889 

717  736  755  774 
908  927  946  965 

7 
8 
9 

13,3 
15,2 

17.1 

229 

984  #003  #021  *040  #069 

#078  #097  #116  *135  *154 

230 

36  173  192  211  229  248 

267 

286  305  324  342 

231. 
232 

361  380  399  418  436 
549  568  586  605  624 

455 
642 

474  493  511  530 
661  680  698  717 

18 

1    1.8 

233 

736  754  773  791  810 

829 

847  866  884  903 

2 

3,6 

234 

922  940  959  977  996 

*014  #033  #051  #070  *088 

3 
4 

5,4 
7,2 

235 

37  107  125  144  162  181 

199 

218  236  254  273 

5 

9,0 

236 

291  310  328  346  365 

383 

401  420  438  457 

6 

10,8 

237 

475  493  511  530  548 

566 

585  603  621  639 

7 
g 

12,6 
14,4 

238 
239 

658  676  694  712  731 
840  858  876  894  912 

749 
931 

767  785  803  822 
949  967  985  *003 

9 

240 

38  021  039  057  075  093 

112 

130  148  166  184 

241 

202  220  238  266  274 

292 

310  328  346  364 

17 

242 

382  399  417  435  '453 

471 

489  507  525  543 

1    1-7 

243 

561  578  596  614  632 

650 

668  686  703  721 

2 

3,4 

244 

739  757  775  792  810 

828 

846  863  881  899 

3 

4 

5,1 
6,8 

245 

917  934  952  970  987 

*005  *023  *041  #058  #076 

5 

8,5 

246 

39  094  111  129  146  164 

182 

199  217  235  252 

6 

10,2 

247 

279  287  305  322  340 

358 

375  393  419  428 

7 
g 

11,9 
13,6 

248 
249 

445  463  480  498  515 
620  637  655  672  690 

533 
707 

650  568  585  602 
724  742  759  777 

9 

15,3 

250 

794  811  829  846  863 

881  898  915  933  950 

N. 

L.  0   1    2   3   4 

5 

6789 

P.  P. 

0°  33'  =  1980"  S.  4.  68  557  T.  4.  68  559 

0°  38'  =  2280"  S.  4.  68  557  T.  4.  68  559 

0  34  =  2040     4.  68  557    4.  68  559 

0  39  =  2340     4.  68  557    4.  68  559 

0  35  =  2100     4.  68  567    4.  68  669 

0  40  =  2400     4.  68  557    4.  68  559 

0  36  =  2160     4.  68  557    4.  68  569 

0  41  =  2460     4.  68  566    4.  68  560 

0  37  =  2220     4.  68  557    4.  68  559 

0  42  =  2520     4.  68  556    4.  68  560 

132          GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

56789 

P.  P. 

250 

39  794  811  829  846  863 

881  898  915  933  950 

251 

967  985  *002  *019  *037 

#054  *071  *088  *106  *123 

18 

252 

40  140  157  175  192  209 

226  243  261  278  295 

1 

1,8 

253 

312  329  346  364  381 

398  415  432  449  466 

2 

3,6 

3 

5,4 

254 

483  500  518  535  552 

569  58G  603  620  637 

4 

7,2 

255 

654  671  688  705  722 

739  756  773  790  807 

5 

9,0 

256 

824  841  858  875  892 

909  926  943  960  976 

6 

10,8 

7 

12,6 

257 

258 

993  #010  *027  *044  *061 
41  162  179  196  212  229 

*078  *095  *111  *128  #145 
246  263  280  296  313 

"8 
9 

14,4 
16,2 

259 

330  347  363  380  397 

414  430  447  464  481 

260 

497  514  531  547  564 

581  597  614  631  647 

261 

664  681  697  714  731 

747  764  780  797  814 

17 

262 

830  847  863  880  896 

913  929  946  963  979 

1 

1/7 

263 

996  #012  *029  *045  *062 

*078  *095  *m  *127  *144 

2 

3,4 

264 

42  160  177  193  210  226 

243  259  275  292  308 

3 
4 

5,1 
6,8 

265 
266 

325  341  357  374  390 
488  504  521  537  553 

406  423  439  455  472 
570  586  602  619  635 

5 
6 

8,5 
10,2 

267 

651  667  684  700  716 

732  749  765  781  797 

7 
3 

11,9 
13,6 

268 
269 

81?  830  846  862  878 
975  991  #008  *§24  #040 

894  911  927  943  959 
*056  *072  *088  *104  #120 

9 

15,3 

270 

43  136  152  169  185  201 

217  233  249  265  281 

271 

297  313  329  345  361 

377  393  409  425  441 

16 

272 

457  473  489  505  521 

537  553  569  584  600 

273 

616  632  648  664  680 

696  712  727  743  759 

1 

1,6 

2 

3/2 

274 

775  791  807  823  838 

854  870  886  902  917 

3 

4,8 

275 

933  949  965  981  996 

#012  *028  *044  *059  *075 

4 

6/4 

276 

44  091  107  122  138  154 

170  185  201  217  232 

5 

8,0 

(j 

9,6 

277 

248  264  279  295  311 

326  342  358  373  389 

7 

11,2 

278 

404  420  436  451  467 

483  498  514  529  545 

8 

12,8 

279 

560  576  592  607  623 

638  654  669  685  700 

9 

14,4 

280 

716  731  747  762  778 

793  809  824  840  855 

281 

871  886  902  917  932 

948  963  979  994  *010 

282 

45  025  040  056  071  086 

10?  117  133  148  163 

15 

283 

179  194  209  225  240 

255  271  286  301  317 

1 

1,5 

2 

3,0 

284 
285  . 

332  347  362  378  393 
484  500  515  530  545 

408  423  439  454  469 
561  576  591  606  621 

3 
4 

4,5 
6,0 

286 

637  652  667  682  697 

712  728  743  758  773 

5 

7,5 

287 

788  803  818  834  849 

864  879  894  909  924 

6 

7 

9,0 
10,5 

288 
289 

939  954  969  984  *000 
46  090  105  120  135  150 

*015  *030  *045  #060  #075 
165  180  195  210  225 

8 
9 

12,0 
13,5 

290 

240  255  270  285  300 

315  330  345  359  374 

291 

389  404  419  434  449 

464  479  494  509  523 

292 
293 

538  553  568  583  598 
687  702  716  731  746 

613  627  642  657  672 
761  776  790  805  820 

1 

14 

1,4 

294 

835  850  864  879  894 

909  923  938  953  967 

2 

2,8 

295 

982  997  *012  *026  *041 

*056  *070  *085  *100  *114 

3 

4,2 

296 

47  129  144  159  173  188 

202  217  232  246  261 

4 
5 

5/6 
7,0 

297 

276  290  305  31?  334 

349  363  378  392  407 

6 

8,4 

298 

422  436  451  465  480 

494  509  524  538  553 

7 

9,8 

299 

567  582  596  611  625 

640  654  669  683  698 

8 

11,2 

9 

12,6 

300 

712  727  741  756  770 

784  799  813  828  842 

N. 

L.  0   1   2   3   4 

56789 

P.  P. 

0°  41'  =  2460"  S.  4.  68  556  T.  4.  68  560    0°  46'  =  2760"  S.  4.  68  556  T.  4.  68  560 

0  42  =  2520    4.  68  556    4.  68  560    0  47  =  2820    4.  68  556    4.  68  560 

0  43  =  2580    4.  68  556    4.  68  560    0  48  =.  2880    4.  68  556    4.  68  560 

0  44  =  2640    4.  68  556    4.  68  560    0  49  =  2940    4.  68  556    4.  68  560 

0  45  =  2700    4.  68  556    4.  68  560    0  50  =  3000    4.  68  556    4.  68  561 

GEOGRAPHIC   TABLES   AND   FORMULAS. 
TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


138 


N. 

L.  0   12   3    4 

5 

6789 

P.P. 

300 

47  712  727  741  756  770 

784 

799  813  828  842 

301 

857  871  885  900  914 

929 

943  958  972  986 

302 

48  001  015  029  044  058 

073 

087  101  116  130 

303 

144  159  173  187  202 

216 

230  244  259  273 

304 

287  302  316  330  344 

359 

373  387  401  416 

15 

306 

430  444  458  473  487 

501 

515  530  544  558 

1 

1,5 

306 

572  586  601  615  629 

643 

657  671  686  700 

2 

3,0 

3 

4,5 

307 

714  728  742  756  770 

785 

799  813  827  841 

4 

6,0 

308 

855  869  883  897  911 

926 

940  954  968  982 

5 

7,5 

309 

996  #010  *024  *038  *052 

*066  *080  *094  #108  #122 

6 

7 

9,0 
10  S 

310 

49  136  150  164  178  192 

206 

220  234  248  262 

8 

-LU/0 

12,0 

311 
312 

276  290  304  318  332 
415  429  443  457  471 

3 

360  374  388  402 
499  513  527  541 

9   13/0 

313 

554  568  582  596  610 

624 

638  651  665  679 

314 

693  707  721  734  748 

762 

776  790  803  817 

315 

831  845  859  872  886 

900 

914  927  941  955 

14. 

316 

969  982  996  *010  *024 

#037  *051  #065  *079  *092 

1   1/4 

317 

50  106  120  133  147  161 

174 

188  202  215  229 

1 

2,8 

318 

243  256  270  284  297 

311 

325  338  352  365 

3 

4,2 

319 

379  393  406  420  433 

447 

461  474  488  501 

4 
5 

5,6 
7,0 

320 

515  529  542  556  569 

583 

596  610  623  637 

6 

8,4 

321 

651  664  678  691  705 

718 

732  745  759  772 

8 

11/2 

322 

786  799  813  826  840 

853 

866  880  893  907 

9 

12,6 

323 

920  934  947  961  974 

987  #001  *014  *028  #041 

324 

51  055  068  081  095  108 

12J 

135  148  162  175 

325 
326 

188  202  215  228  242 
322  335  348  362  375 

255 
388 

268  282  295  308 
402  415  428  441 

327 

455  468  481  495  508 

521 

534  548  561  574 

13 

328 

587  601  614  627  640 

654 

667  680  693  706 

1 

1,3 

329 

720  733  746  759  772 

786 

799  812  825  838 

2 

2/6 

q  Q 

330 

851  865  878  891  904 

917 

930  943  957  970 

4 

o/y 
5/2 

331 

332 

983  996  #009  *022  *035 
52  114  127  140  153  166 

*048  *061  #075  *088  *101 
179  192  205  218  231 

5 
6 

6/6 
7,8 
9/1 

333 

244  257  270  284  297 

310 

323  336  349  362 

8 

10/4 

334 

375  388  401  414  427 

440 

453  466  479  492 

9 

11,7 

335 

504  517  530  543  556 

569 

582  595  608  621 

336 

634  647  660  673  686 

699 

711  724  737  750 

337 

763  776  789  802  815 

827 

840  853  866  879 

338 
339 

892  905  917  930  943 
53  020  033  046  058  071 

956 
084 

969  982  994  *007 
097  110  122  135 

12 

340 

148  161  173  186  199 

212 

224  237  250  263 

1 

1.2 

2 

2,4 

341 

275  288  301  314  326 

339 

352  364  377  390 

3 

3,6 

342 
343 

403  415  428  441  453 
529  542  555  567  580 

466 
693 

479  491  504  517 
605  618  631  643 

4 

5 

4,8 
6,0 

6 

7,2 

344 

656  668  681  694  706 

719 

732  744  757  769 

7 

8,4 

345 
346 

782  794  807  820  832 
908  920  933  945  958 

845 
970 

857  870  882  895 
983  995  *OOS  *020 

8 
9 

9,6 
10,8 

347 

348 

54  033  045  058  070  083 
158  170  183  195  208 

095 
220 

108  120  133  145 
233  245  258  270 

349 

283  295  307  320  332 

345 

357  370  382  394 

350 

407  419  432  444  456 

469 

481  494  506  518 

N. 

L.  0   1   2   3   4 

5 

6,7   8   9 

P.  P. 

0°  50'  =  3000"  S.  4.  68  556  T.  4.  68  561 

0°  55'  =  3300"  S.4.  68  556  T.4.  68  561 

0  51  =  3060     4.  68  556    4.  68  561 

0  56  =  3360    4.  68  55?    4.  38  561 

0  52  =  3120     4.  68  556    4.  68  561 

0  57  =  3420    4.  68  555    4.  68  561 

0  53  =  3180     4.  68  556    4.  68  561 

0  58  =  3480    4.  68  555    4.  68  562 

0  54  =*  3240     4.  68  556    4.  68  561 

0  59  =  3540    4.  68  555    4.  68  562 

134  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

56789 

P.P. 

350 

54  407  419  432  444  456 

469  481  494  506  518 

351 
352 

531  543  555  568  580 
654  667  679  691  704 

593  605  617  630  642 
716  728  741  753  765 

353 

777  790  802  814  827 

839  851  864  876  888 

13 

354 

900  913  925  937  949 

962  974  986  998  *011 

355 

55  023  035  047  060  072 

084  096  108  121  133 

O  £ 

356 

145  157  169  182  194 

206  218  230  242  255 

3 

2,b 
3,9 

357 

267  279  291  303  315 

328  340  352  364  376 

4 

5,2 

358 

388  400  413  425  437 

449  461  473  485  497 

5 

6,5 

359 

509  522  534  546  558 

570  582  594  606  618 

6 

7 

7,8 
9,1 

360 

630  642  654  666  678 

691  703  715  .  727  739 

8 

10,4 

9 

11,7 

361 

751  763  775  787  799 

811  823  835  847  859 

362 

871  883  895  907  919 

931  943  955  967  979 

363 

991  *003  #015  *027  #038 

*050  *062  *074  *086  #098 

364 
365 

56  110  122  134  146  158 
229  241  253  265  277 

170  182  194  205  217 
289  301  312  324  336 

1  O 

366 

348  360  372  384  3% 

407  419  431  443  455 

IB 

1 

1/2 

367 

467  478  490  502  514 

526  538  549  561  573 

2 

2,4 

368 
369 

585  597  608  620  632 
703  714  726  738  750 

644  656  667  679  691 
761  773  785  797  808 

3 

4 

3,6 

4,8 

370 

5 
6 

6,0 
7,2 

820  832  844  855  867 

879  891  902  914  926 

371 

937  949  961  972  984 

996  *008  *019  *031  #043 

7 

8,4 

O  A 

372 

57  054  066  078  089  101 

113  124  136  148  159 

y/t> 

10  ft 

373 

171  183  194  206  217 

229  241  252  264  276 

-iU/o 

374 

287  299  310  322  334 

345  357  368  380  392 

375 
376 

403  415  426  438  449 
519  530  542  553  565 

461  473  484  496  507 
576  588  600  611  623 

377 

634  646  657  669  680 

692  703  715  726  738 

11 

378 

749  761  772  784  795 

807  818  830  841  852 

1 

1/1 

379 

864  875  887  898  910 

921  933  944  955  967 

2 

2,2 

O  Q 

380 

978  990  *001  *013  *024 

*035  *047  *058  *070  *081 

4 

o/o 
4,4 

381 

58  092  104  115  127  138 

149  161  172  184  195 

5 

5,5 

A  A 

382 

206  218  229  240  252 

263  274  286  297  309 

O,O 

383 

320  331  343  354  365 

377  388  399  410  422 

8 

8,8 

384 
386 
386 

433  444  456  467  478 
546  557  569  580  591 
659  670  681  692  704 

490  501  512  524  535 
602  614  625  636  647 
715  726  737  749  760 

9 

9,9 

387 

771  782  794  805  816 

827  838  850  861  872 

388 

883  894  906  917  928 

939  950  961  973  984 

1  f\ 

389 

995  *006  *017  *028  *040 

*051  #062  *073  *084  #095 

J.U 

i  n 

390 

59  106  118  129  140  151 

162  173  184  195  207 

. 

2 

J./U 

2,0 

391 

218  229  240  251  262 

273  284  295  306  318 

3 
4 

3,0 

392 
393 

329  340  351  362  373 
439  450  461  472  483 

384  395  406  417  428 
494  506  517  528  539 

5 
6 

5^0 
6,0 

394 

550  561  572  583  594 

605  616  627  638  649 

7 

7,0 
o  fi 

395 

660  671  682  693  704 

715  726  737  748  759 

o/U 
q  n 

396 

770  780  791  802  813 

824  835  846  857  868 

y/u 

397 

879  890  901  912  923 

934  945  956  966  977 

398 

988  999  *010  *021  #032 

*043  *054  ,066  *076  *086 

399 

60  097  108  119  130  141 

152  163  173  184  195 

400 

206  217  228  239  249 

260  271  282  293  304 

s. 

L.  0   1    2    3    4 

56789 

P.P. 

OP  58'  =  3480"  S.  4.  68  555  T.  4.  68  562    1°  3'  =  3780"   S.  4.  68  555  T.  4.  68  562 

0  59  =  3540     4.  68  555    4.  68  562    14=  3840     4.  68  555    4.  68  563 

10=  3600     4.  68  555    4.  68  562    15=  3900     4.  68  555    4.  68  563 

11=  3660  "    4.  68  555    4.  68  562    16=  3960     4.  68  555    4.  68  563 

12=  3720    4.  68  555    4.  68  562    17=  4020     4.  68  555    4.  68  563 

GEOGKAPHIC    TABLES    AJSTD    FORMULAS.  135 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1    2   3   4 

5 

6789 

P 

.  P. 

400 

60  206  217  228  239  249 

260 

271  282  293  304 

401 

314  325  336  347  358 

369 

379  390  401  412 

402 

423  433  444  455  466 

477 

487  498  509  520 

403 

531  541  552  563  574 

584 

595  606  617  627 

404 

638  649  660  670  681 

692 

703  713  724  735 

405 

746  756  767  778  788 

799 

810  821  831  842 

406 

853  863  874  885  895 

906 

917  927  938  949 

11 

407 

959  970  981  991  *002 

#013  *023  *034  *045  *055 

1 

1/1 

408 

61  066  077  087  098  109 

119 

130  140  151  162 

2 

2,2 

409 

172  183  194  204  215 

225 

236  247  257  268 

3 

3,3 

410 

278  289  300  310  321 

331 

342  352  363  374 

4 
5 

4,4 

5,5 

411 

384  395  405  416  426 

437 

448  458  469  479 

6 

6,6 

412 
413 

490  500  511  521  532 
595  606  616  627  637 

542 

648 

553  563  574  584 
658  669  679  690 

7 
8 
9 

7,7 
8,8 
9,9 

414 
415 

700  711  721  731  742 

805  815  826  836  847 

752 

857 

763  773  784  794 
868  878  888  899 

416 

909  920  930  941  951 

962 

972  982  993  *003 

417 

62  014  024  034  045  055 

066 

076  086  097  107 

418 

118  128  138  149  159 

170 

180  190  201  211 

419 

221  232  242  252  263 

273 

284  294  304  315 

420 

325  335  346  356  366 

377 

387  397  408  418 

421 

428  439  449  459  469 

480 

490  500  511  521 

10 

422 
423 

531  542  552  562  572 
634  644  655  665  675 

583 
685 

593  603  613  624 
696  706  716  726 

1 
2 

1/0 
2,0 

3 

3,0 

424 

737  747  757  767  778 

788 

798  808  818  829 

4 

4,0 

425 

839  849  859  870  880 

890 

900  910  921  931 

5 

5,0 

426 

941  951  961  972  982 

992  *002  #012  *022  *033 

6 

6,0 

7 

7,0 

427 

63  043  053  063  073  083 

094 

104  114  124  134 

8 

8,0 

428 

144  155  165  175  185 

195 

205  215  225  236 

9 

9,0 

429 

246  256  266  276  286 

296 

306  317  327  337 

430 

347  357  367  377  387 

397 

407  417  428  438 

431 

448  458  468  478  488 

498 

508  518  528  538 

432 

548  558  568  579  589 

599 

609  619  629  639 

433 

649  659  669  679  689 

699 

709  719  729  739 

434 

749  759  769  779  789 

799 

809  819  829  839 

435 

849  859  869  879  889 

899 

909  919  929  939 

436 

949  959  969  979  988 

998  *008  #018  *028  *038 

9 

437 

64  048  058  068  078  088 

098 

108  118  128  137 

1 

0,9 

438 

147  157  167  177  187 

197 

207  217  227  237 

2 

1,8 

439 

246  256  266  276  286 

2% 

306  316  -326  335 

3 

4 

2,7 
3,6 

440 

345  355  365  375  385 

395 

404  414  424  434 

5 
6 

4,5 

5,4 

441 

444  454  464  473  483 

493 

503  513  523  532 

7 

6,3 

442 
443 

542  552  562  572  582 
640  650  660  670  680 

591 
689 

601  611  621  631 
699  709  719  729 

8 
9 

7,2 
8,1 

444 

445 

738  748  758  768  777 
836  846  856  865  875 

11 

797  807  816  826 
895  904  914  924 

446 

933  943  953  963  972 

982 

992  #002  *011  *021 

447 

65  031  040  050  060  070 

079 

089  099  108  118 

448 

128  137  147  157  167 

176 

186  196  205  215 

449 

225  234  244  254  263 

273 

283  292  302  312 

450 

321  331  341  350  360 

369 

379  389  398  408 

N. 

L.  0   1   2   3   4 

5 

6789 

P.  P. 

1°  6'  =  3960"  S.  4.  68  555  T.  4.  68  563 

1°  11'=  4260"  S.  4.  68  554  T.  .68  564 

1   7  =  4020    4.  68  555    4.  68  563 

1  12  =  4320    4.  68  554 

.  68  564 

1   8  =  4080    4.  68  555    4.  68  563 

1  13  =  4380    4.  68  554 

.  68  564 

1   9  =  4140    4.  68  555    4.  68  563 

1  14  =  4440    4.  68  554 

.  68  664 

1  10  =  4200    4.  68  554    4.  68  563 

1  15  =  4500    4.  68  554 

.  68  564 

136  GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.   0   1   2   3    4 

5 

6789 

P.P. 

450 

65  321  331  341  350  360 

369  379  389  398  408 

451 

418  427  437  447  456 

466  475  485  495  504 

452 

514  523  533  543  552 

562 

371  581  591  600 

453 

610  619  629  639  648 

658  667  677  686  696 

464 

706  715  725  734  744 

753  763  772  782  792 

455 

801  811  820  830  839 

849 

*58  868  877  887 

456 

896  906  916  925  935 

944  954  963  973  982 

10 

457 

992  #001  *011  *020  *030 

*039  *049  *058  *068  *077 

1  1,0 

458 

66  087  096  106  115  124 

134 

L43  153  162  172 

2  2,0 

459 

181  191  200  210  219 

229  238  247  257  266 

3  3,0 

460 

276  285  295  304  314 

323  332  342  351  361 

4  4,0 
5  5,0 

461 

370  380  389  398  408 

417  427  436  445  455 

6  6,0 

462 

464  474  483  492  502 

511 

321  530  539  549 

7  7,0 

463 

558  567  577  586  596 

605  614  624  633  642 

8  8,0 
9  9,0 

464 
465 

652  661  671  680  689 
745  755  764  773  783 

699  708  717  727  736 
792  801  811  820  829 

466 

839  848  857  867  876 

885  894  904  913  922 

467 

932  941  950  960  969 

978  987  997  *006  *015 

468 

67  025  034  043  052  062 

071  080  089  099  108 

469 

117  127  136  145  154 

164 

173  182  191  201 

470 

210  219  228  237  247 

256  265  274  284  293 

471 

302  311  321  330  339 

348  357  367  376  385 

9 

472 
473 

394  403  413  422  431 
486  495  504  514  523 

440  449  459  468  477 
532  541  550  560  569 

1  0,9 
2  1,8 

3  2,7 

474 

678  587  596  605  614 

624  633  642  651  660 

4  3,6 

475 

669  679  688  697  706 

715 

724  733  742  752 

5  4,5 

476 

761  770  779  788  797 

806 

S15  825  834  843 

6  5,4 

7  6,3 

477 

852  861  870  879  888 

897  906  916  925  934 

8  7,2 

478 

943  952  961  970  979 

988 

997  *006  *015  *024 

9  8,1 

479 

68  034  043  052  061  070 

079  088  '097  '106  '115 

480 

124  133  142  151  160 

169  178  187  196  205 

481 

482 

215  224  233  242  251 
305  314  323  332  341 

260  269  278  287  296 
350  359  368  377  386 

483 

395  404  413  422  431 

440  449  458  467  476 

484 

485  494  502  511  520 

629  538  547  556  565 

485 

674  583  592  601  610 

619  628  637  646  655 

486 

664  673  681  690  699 

708  717  726  735  744 

8 

487 

753  762  771  780  789 

797 

806  815  824  833 

1  0,8 
2  1,6 

488 

842  851  860  869  878 

886 

895  904  913  922 

489 

931  940  949  958  966 

975  984  993  *002  t011 

4  3^2 

490 

69  020  028  037  046  055 

064  073  082  090  099 

5  4,0 

6  4,8 

491 

108  117  126  135  144 

152 

161  170  179  188 

7  5,6 

492 

197  205  214  223  232 

241 

249  258  267  276 

8  6,4 

493 

285  294  302  311  320 

329 

338  346  355  364 

9  7,2 

494 

373  381  390  399  408 

417 

425  434  443  452 

495 

461  469  478  487  496 

504 

513  522  531  539 

496 

548  557  566  674  583 

592 

601  609  618  627 

497 

636  644  653  662  671 

679 

688  697  705  714 

498 
499 

723  732  740  749  758 
810  819  827  836  845 

767 

854 

775  784  793  801 
862  871  880  888 

500 

897  906  914  923  932 

940 

949  958  966  975 

N. 

L.   0   1   2   3    4 

5 

6789 

P.  P. 

1°  15'=  4600"  S.  4.  68  564  T.  4.  68  564 
1  16  =  4560     4.  68  564    4.  68  565 

1°  20'=  4800"  S.  4.  68  554  T.  4.  68  566 
1  21  =  4860     4.  68  553    4.  68  566 

1  17  =  4620     4.  68  554    4.  68  565 

1  22  =  4920     4.  68  553    4.  68  566 

1  18  =  4680     4.  68  554    4.  68  565 

1  23  =  4980     4.  68  553    4.  68  566 

1  19  =  4740     4.  68  554    4.  68  565 

1  24  =  5040     4.  68  653    4.  68  566 

GEOGRAPHIC    TABLES    AND   FORMULAS. 
TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


137 


N. 

L.  0   1   2   3   4 

5 

6789 

P. 

P. 

500 

69  897  906  914  923  932 

940 

949  958  966  975 

501 

984.  992*001  *010  *018 

*027* 

036  *044  *053  *062 

502 

70  070  079  088  096  105 

114 

122  131  140  148 

503 

157  165  174  183  191 

200 

209  217  226  234 

504 

243  252  260  269  278 

286 

295  303  312  321 

505 
506 

329  338  346  355  364 
415  424  432  441  449 

372 
458 

381  389  398  406 
467  475  484  492 

507 

508 

501  509  518  526  535 
586  595  603  612  621 

544 

629 

552  561  569  578 
638  646  655  663 

9 

509 

672  680  689  697  706 

714 

723  731  740  749 

1 
2 

0,9 
1/8 

510 

757  766  774  783  791 

800  808  817  825  834 

3 

2,7 

511 
512 

4 
5 
6 

3,6 
4/5 
5,4 

842  851  859  868  876 
927  935  944  952  961 

885  893  902  910  919- 
969  978  986  995  *003 

513 

71  012  020  029  037  046 

054  063  071  079  088 

7 

6,3 

514 

096  105  113  122  130 

139 

147  155  164  172 

8 
9 

7,2 

8,1 

515 
516 

181  189  198  206  214 
265  273  282  290  299 

223 
307 

231  240  248  257 
315  324  332  341 

517 
518 

349  357  366  374  383 
433  441  450  458  466 

391 
475 

399  408  416  425 
483  492  500  508 

619 

517  525  533  542  550 

559 

567  575  684  592 

520 

6CO  609  617  625  634 

642 

650  659  667  675 

521 
522 
623 

684  692  700  709  717 
767  775  784  792  800 
a50  858  867  875  883 

725 

809 
892 

734  742  750  759 
817  825  834  842 
900  908  917  925 

1 
2 

8 

0,8 
1,6 

524 

933  941  950  958  966 

975  983  991  999  *008 

3 
4 

2,4 
3,2 

525 

72  016  024  032  041  049 

057 

066  074  082  090 

5 

4,0 

526 

099  107  115  123  132 

140 

148  156  165  173 

6 

4,8 

7 

5,6 

527 

181  189  198  206  214 

222 

230  239  247  265 

8 

6,4 

528 
529 

263  272  280  288  296 
346  354  362  370  378 

304 
387 

313  321  329  337 
395  403  411  419 

9 

7,2 

530 

428  436  444  452  460 

469 

477  485  493  501 

531 

509  518  526  534  542 

550 

558  567  575  583 

532 
533 

591  599  607  616  624 
673  681  689  697  705 

632 
713 

640  648  656  665 
722  730  738  746 

534 

754  762  770  779  787 

795 

803  811  819  827 

635 
536 

835  843  852  860  868 
916  925  933  941  949 

876 
957 

884  892  900  908 
965  973  981  989 

7 

537 

997  *006  *014  *022  *030 

*038  *046  *054  *062  *070 

1 

0,7 

538 

73  078  086  094  102  111 

119 

127  135  143  151 

2 

1/4 

539 

159  167  175  183  191 

199  207  215  223  231 

3 

2,1 

540 

239  247  255  263  272 

280  288  296  304  312 

5 

3,5 

541 

320  328  336  344  352 

360  368  376  384  392 

6 

4,2 

542 

400  408  416  424  432 

440 

448  456  464  472 

7 

4,9 

C  f» 

543 

480  488  496  504  512 

520  528  536  544  552 

9 

0,0 
6,3 

544 

560  568  576  584  592 

600 

608  616  624  632 

545 

640  648  656  664  672 

679 

687  695  703  711 

646 

719  727  735  743  751 

759 

767  775  783  791 

547 

799  807  815  823  830 

838 

846  854  862  870 

548 

878  886  894  902  910 

918 

926  933  941  949 

549 

957  965  973  981  989 

997* 

005  *013  *020  *028 

550 

74  036  044  052  060  068 

076 

084  092  099  107 

N. 

L.  0   1   2   3   4 

5 

6789 

P. 

P. 

1°  23'=  4980"  S.  4.  68  553  T.  4.  68  566 

1°  28'=  5280"  S.  4.  68  553  T.  4.  68  567 

1  24  =  5040     4.  68  553    4.  68  566 

1  29  =  5340  '   4.  68  553 

4.  68  667 

1  25  =  5100     4.  68  553    4.  68  566 

1  30  =  5400     4.  68  553 

4.  68  567 

1  26  =  5160     4.  68  553    4.  68  567 

1  31  =  5460     4.  68  552 

4.  68  668 

1  27  =  5220    4.  68  653    4.  68  567 

1  32  =  5520     4.  68  552 

4.  68  668 

138  GEOGRAPHIC   TABLES    AND    FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

5 

6789 

P.  P. 

550 

74  036  044  052  060  068 

076  084  092  099  107 

551 

115  123  131  139  147 

155  162  170  178  186 

552 
553 

194  202  210  218  225 
273  280  288  296  304 

233  241  249  257  265 
312  320  327  335  343 

554 
565 
556 

351  359  367  374  382 
429  437  445  453  461 
607  515  523  531  539 

390  398  406  414  421 
468  476  484  492  500 
547  554  562  570  578 

557 

586  593  601  609  617 
663  671  679  687  695 

624  632  640  648  656 
702  710  718  726  733 

559 

741  749  757  764  772 

780  788  796  803  811 

560 

819  827  834  842  850 

858  865  873  881  889 

561 

896  904  912  920  927 

935  943  950  958  966 

562 

974  981  989  997  *005 

*012  * 

320  *028  *035  *043 

8 

563 

75  051  059  066  074  082 

089  097  105  113  120 

1 

0,8 

2 

1,6 

564 

128  136  143  151  159 

166  174  182  189  197 

3 

2,4 

565 

205  213  220  228  236 

243 

251  259  266  274 

4 

3,2 

566 

282  289  297  305  312 

320  328  335  343  351 

5 

4,0 

6 

4,8 

567 
568 

358  366  374  381  389 
435  442  450  458  465 

397  404  412  420  427 
473  481  488  496  504 

8 

5,6 
6,4 

569 

611  519  526  634  542 

549  557  565  572  580 

9 

7,2 

570 

687  595  603  610  618 

626  633  641  648  656 

571 

664  671  679  686  694 

702  709  717  724  732 

572 
573 

740  747  755  762  770 
815  823  831  838  846 

778  785  793  800  808 
853  861  868  876  884 

574 

891  899  906  914  921 

929  937  944  952  959 

575 

967  974  982  989  997 

*005  *( 

312  *020  *027  *035 

576 

76  042  050  057  065  072 

080  087  095  103  110 

577 

118  125  133  140  148 

155  163  170  178  185 

578 
579 

193  200  208  215  223 
268  275  283  290  298 

230  238  245  253  260 
305  313  320  328  335 

580 

343  350  358  365  373 

380  388  395  403  410 

581 

582 

418  425  433  440  448 
492  500  507  515  522 

456  462  470  477  485 
530  537  545  552  559 

7 

583 

567  574  582  589  597 

604  612  619  626  634 

1 

0,7 

2 

1/4 

584 

585 

641  649  656  664  671 
716  723  730  738  745 

678  686  693  701  708 
753  760  768  775  782 

3 
4 

2,1 

2,8 

586 

790  797  805  812  819 

827  834  842  849  856 

5 

3,5 

6 

4,2 

587 
588 

864  871  879  886  893 
938  945  953  960  967 

901  908  916  923  930 
975  982  989  997  *004 

7 
8 

4,9 
5,6 

589 

77  012  019  026  034  041 

048  056  063  070  078 

9 

6,3 

590 

085  093  100  107  115 

122  129  137  144  151 

591 

159  166  173  181  188 

195  203  210  217  225 

592 

232  240  247  254  262 

269  276  283  291  298 

593 

305  313  320  327  335 

342  349  357  364  371 

594 

'  595 

379  386  393  401  408 
452  459  466  474  481 

415  422  430  437  444 

488  495  503  510  517 

596 

525  532  539  54fc  554 

561  568  576  583  590 

597 

597  605  612  619  627 

634  641  648  656  663 

598 

670  677  685  692  699 

706  714  721  728  735 

599 

743  750  757  764  772 

779  786  793  801  808 

600 

815  822  830  837  844 

851  859  866  873  880 

N. 

L.  0   1   2   3   4 

5 

6789 

P.P. 

1°  31'  =  5460"  S.  4.  68  552  T.  4.  68  568 

1°  36'  =  5760"  S.  4.  68  562  T.  4.  68  569 

1  32  =  5520    4.  68  552    4.  68  568 

1  37  =  5820     4.  68  552 

4.  68  569 

1  33  =  6580    4.  68  552    4.  68  568 

1  38  =  5880    4.  68  552 

4.  68  669 

1  34  =  5640    4.  68  552    4.  68  568 

1  39  =  5940     4.  68  551 

4.  68  569 

1  35  =  5700     4.  68  552    4.  68  669 

1  40  =  6000     4.  68  551 

4.  68  570 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


139 


N; 

L.  0   1   2   3   4 

5 

6789 

P 

P. 

600 

77  815  822  830  837  844 

851 

859  866  873  880 

601 

887  895  902  909  916 

924 

931  938  945  952 

602 

960  967  974  981  988 

9%  * 

003  *010  $017  *025 

603 

78  032  039  046  053  061 

068 

075  082  089  097 

604 

104  111  118  125  132 

140 

147  154  161  168 

605 

176  183  190  197  204 

211 

219  226  233  240 

606 

247  254  262  269  276 

283 

290  297  305  312 

8 

607 

608 

319  326  333  340  347 

390  398  405  412  419 

355 
426 

362  369  376  383 
433  440  447  455 

1 

2 

0,8 

1,6 

609 

462  469  476  483  490 

497 

504  512  519  526 

3 

2,4 

610 

633  540  547  554  561 

569 

576  583  590  597 

4 

5 

3,2 
4,0 

611 
612 

604  611  618  625  633 
675  682  689  696  704 

640 
711 

647  654  661  668 

718  725  732  739 

6 

7 

4,8 
5,6 

613 

746  753  760  767  774 

781 

789  796  803  810 

8 
9 

6,4 
7,2 

614 

817  824  831  838  845 

852 

859  866  873  880 

615 

888  895  902  909  916 

923 

930  937  944  951 

616 

958  965  972  979  986 

993  *000  *007  *014  *021 

617 

79  029  036  043  050  057 

064 

071  078  085  092 

618 

099  106  113  120  127 

134 

141  148  155  162 

619 

169  176  183  190  197 

204 

211  218  225  232 

620 

239  246  253  260  267 

274 

281  288  295  302 

621 

309  316  323  330  337 

344 

351  358  365  372 

7 

622 

379  386  393  400  407 

414 

421  428  435  442 

I 

0  7 

623 

449  456  463  470  477 

484 

491  498  505  511 

2 

1/4 

624 

518  625  532  539  546 

653 

560  567  574  581 

3 

A 

2,1 

0  v 

625 

588  595  602  609  616 

623 

630  637  644  650 

5 

&r& 
3  5 

626 

667  664  671  678  685 

692 

699  706  713  720 

6 

OfO 

4,2 

627 

727  734  741  748  754 

761 

768  775  782  789 

7 
'  g 

4,9 
56 

628 

7%  808  810  817  824 

831 

837  844  851  858 

cf/D 
6  ^ 

629 

865  872  879  886  893 

900 

906  913  920  927 

o/o 

630 

934  941  948  956  962 

969  975  982  989  996 

631 

80  003  010  017  024  030 

037 

044  051  058  065 

632 
633 

072  079  085  092  099 
140  147  154  161  168 

106 
175 

113  120  127  134 
182  188  195  202 

634 

209  216  223  229  236 

243 

250  257  264  271 

635 

277  284  291  298  305 

312 

318  325  332  339 

636 

346  353  359  366  373 

380 

387  393  400  407 

6 

637 

414  421  428  434  441 

448 

455  462  468  475 

1 

0,6 

638 

482  489  496  502  509 

516 

523  530  536  543 

2 

1,2 

639 

550  557  564  570  577 

584 

591  598  604  611 

3 

1/8 

640 

618  626  632  638  646 

652 

669  665  672  679 

4 
5 

2,4 
3,0 

641 

686  693  699  706  713 

720 

726  733  740  747 

6 

3,6 

642 
643 

754  760  767  774  781 
821  828  835  841  848 

794  801  80§  814 
862  868  875  882 

7 
8 
9 

4,2 

4,8 
5,4 

644 

889  895  902  909  916 

922 

929  936  943  949 

645 
646 

956  963  969  976  983 
81  023  030  037  043  050 

990 
057 

996  #003  *010  *017 
064  070  077  084 

647 

090  097  104  111  117 

124 

131  137  144  151 

648 

158  164  171  178  184 

191 

198  204  211  218 

649 

224  231  238  245  251 

258 

265  271  278  285 

650 

291  298  305  311  318 

325 

331  338  345  351 

N. 

L.  0   1   2   3   4 

5 

6789 

P 

P. 

0  407  =  6000"  S.  4.  68  551  T.  4.  68  570 

1°  45'  =  6300"  S.  4.  68  551  T 

.  4.  68  571 

41  =  6060    4.  68  551    4.  68  570 

1  46  =»  6360    4.  68  551 

4.  68  571 

42  =  6120    4.  68  551    4.  68  570 

1  47  =  6420    4.  68  5i?0 

4.  68  572 

43  =  6180    4.  68  561    4.  68  570 

1  48  =.  6480    4.  68  5$0 

4.  68  572 

44  =  6240    4.  68  661    4.  68  671 

1  49  =  6540    4.  68  550 

4.  68  572 

140  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

5 

6789 

P.  P. 

650 

81  291  298  305  311  318 

325  « 

531  338  345  351 

651 
652 
653 

358  365  371  378  385 
425  431  438  445  451 
491  498  505  511  518 

391  398  405  411  418 
458  465  471  478  485 
525  531  538  544  551 

664 

558  564  571  578  584 

591  598  604  611  617 

655 
666 

624  631  637  644  651 
690  697  704  710  717 

657  664  671  677  684 
723  730  737  743  750 

657 
658 

757  763  770  776  783 

823  829  836  842  849 

790  796  803  809  816 

856  862  869  875  882 

659 

889  895  902  908  915 

921  928  935  941  948 

660 

954  961  968  974  981 

987  < 

)94  #000  *007  *014 

661 

82  020  027  033  040  046 

053  ( 

)60  066  073  079 

7 

662 

086  092  099  105  112 

119  i 

125  132  138  145 

663 

151  158  164  171  178 

184  191  197  204  210 

1  0,7 
2  1,4 

664 

217  223  230  236  243 

249  256  263  269  276 

3  2,1 

665 

282  289  295  302  308 

315  : 

J21  328  334  341 

4  2,8 

666 

347  354  360  367  373 

380  387  393  400  406 

5  3,5 
6  4,2 

667 

413  419  426  432  439 

445  452  458  465  471 

7  4,9 

668 

478  484  491  497  604 

510  , 

)17  523  530  536 

8  6,6 

669 

543  549  556  662  569 

575  582  588  595  601 

9  6,3 

670 

607  614  620  627  633 

640  ( 

>46  653  659  666 

671 
672 

672  679  685  692  698 
737  743  750  756  763 

705  711  718  724  730 

769  776  782  789  795 

673 

802  808  814  821  827 

834  840  847  853  860 

674 

866  872  879  885  892 

898  905  911  918  924 

675 

930  937  943  950  956 

963 

»9  975  982  988 

676 

995  #001  *008  #014  *020 

*027*< 

)33  #040  #046  #052 

677 

83  059  065  072  078  085 

091  097  104  110  117 

678 

123  129  136  142  149 

155 

L61  168  174  181 

679 

187  193  200  206  213 

219  ' 

225  232  238  245 

680 

251  257  264  270  276 

283  289  296  302  308 

681 

315  321  327  334  340 

347  353  359  366  372 

6 

682 
683 

378  385  391  398  404 
442  448  455  461  467 

410  417  423  429  436 
474  480  487  493  499 

1  0,6 
2  1,2 

684 

506  512  518  525  531 

537  544  550  556  563 

3  1,8 
4  2,4 

685 

569  575  582  588  594 

601  607  613  620  626 

5  3,0 

686 

632  639  645  651  658 

664  670  677  683  689 

6  3,6 

687 

696  702  708  715  721 

727  734  740  746  753 

7  4,2 
8  48 

688 
689 

759  765  771  778  784 
822  828  835  841  847 

790  797  803  809  816 
853  860  866  872  879 

9  5,4 

690 

885  891  897  904  910 

916 

83  929  935  942 

691 

948  954  960  967  973 

979  < 

J85  992  998  *004 

692 
693 

84  Oil  017  023  029  036 
073  080  086  092  098 

042  048  055  061  '067 
105  111  117  123  130 

694 

136  142  148  155  161 

167  173  180  186  192 

695 

198  205  211  217  223 

230  ' 

236  242  248  255 

696 

261  267  273  280  286 

292  298  305  311  317 

697 

323  330  336  342  348 

354  361  367  373  379 

698 

386  392  398  404  410 

417 

123  429  435  442 

699 

448  454  460  466  473 

479  485  491  497  504 

700 

510  516  522  528  535 

541  547  553  559  566 

N. 

L.  0   1   2   3   4 

5 

6789 

P.  P. 

1°  48'  =?  6480"  S.  4.  68  550  T.  4.  68  572 

10  53/  =  6780"  S.  4.  68  550  T.  4.  68  573 

1  49  =  6540     4.  68  550    4.  68  572 

1  54  =  6840     4.  68  650    4.  68  573 

1  50  =  6600     4.  68  550    4.  68  572 

1  55  =  6900     4.  68  649    4.  68  574 

1  51  =  6660     4.  68  550    4.  68  673 

1  66  =  6960     4.  68  549    4.  68  674 

1  52  =  6720     4.  68  650    4.  68  573 

1  57  =  7020     4.  68  549    4.  68  574 

GEOGRAPHIC   TABLES   AND   FORMULAS. 
TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


141 


N. 

L.  0   1   2   3   4 

5   6   7   8   9 

P.P. 

700 

701 
702 
703 

704 

705 
706 

707 
708 
709 

710 

711 
712 
713 

714 
715 
716 

717 

718 
719 

720 

721 
722 
.  723 

724 
725 
726 

727 
728 
729 

730 

731 
732 
733 

734 
735 
736 

737 
738 
739 

740 

741 
742 
743 

744 

745 
746 

747 
748 
749 

760 

84  510  516  522  528  535 

541  547  553  559  566 

7 

1  0/7 
2  1/4 
3  2,1 
4  2,8 
5  3,5 
6  4,2 
7  4,9. 
8  5,6 
9  6,3 

B 

1  0,6 
2  1,2 
3  1,8 
4  2,4 
5  3,0 
6  3,6 
7  4,2 
8  4,8 
9  5,4 

5 

1  0,5 
2  1,0 
3  1,5 
4  2,0 
5  2,5 
6  3,0 
7  3,5 
8  4,0 
9  4,5 

572  578  584  590  597 
634  640  646  652  658 
696  702  708  714  720 

757  763  770  776  782 
819  825  831  837  844 
880  887  893  899  905 

942  948  954  960  967 
85  003  009  016  022  028 
065  071  077  083  089 

603  609  61&  621  628 
665  671  677  683  689 
726  733  739  745  751 

788  794  800  807  813 
850  856  862  868  874 
911  917  924  930  936 

973  979  985  991  997 
034  040  046  052  058 
095  101  107  114  120 

126  132  138  144  150 

156  163  169  175  181 

187  193  199  205  211 
248  254  260  266  272 
309  315  321  327  333 

370  376  382  388  394 
431  437  443  449  455 
491  497  503  509  616 

552  558  564  570  576 
612  618  625  631  637 
673  679  685  691  697 

217  224  230  236  242 
278  285  291  297  303 
339  345  352  358  364 

400  406  412  418  42§ 
461  467  473  479  485 
522  528  534  540  646 

582  588  594  600  606 
643  649  65^  661  667 
703  709  715  721  727 

733  739  745  751  757 

763  769  775  781  788 

794  800  806  812  818 
854  860  866  872  878 
914  920  926  932  938 

974  980  986  992  998 
86  034  040  046  052  058 
094  100  106  112  118 

153  159  165  171  177 
213  219  225  231  237 
273  279  285  291  297 

824  830  836  842  848 
884  890  896  902  908 
944  950  956  962  968 

*004  *010  #016  #022  *028 
064  070  076  082  088 
124  130  136  141  147 

183  189  195  201  207 
243  249  255  261  267 
303  308  314  320  326 

332  338  344  350  356 

362  368  374  380  386 

392  398  404  410  416. 
451  457  463  469  475 
510  516  522  528  534 

570  576  581  587  593 
629  635  641  646  652 
688  694  700  705  711 

7*7  753  759  764  770 
806  812  817  823  829 
864  870  876  882  888 

421  427  433  439  445 
481  487  493  499  504 
540  546  552  558  564 

599  605  611  617  623 
658  664  670  676  682 
717  723  729  735  741 

776  782  788  794  800 
835  841  847  853  859 
894  900  906  911  917 

923  929  935  941  947 

953  958  964  970  976 

982  988  994  999  *005 
87  040  046  052  058  064 
099  105  111  116  122 

157  163  169  175  181 
216  221  227  233  239 
274  280  286  291  297 

332  338  344  349  355 
390  396  402  408  413 
448  454  460  466  471 

*011  *017  #023  *029  #035 
070  075  081  087  093 
128  134  140  146  151 

186  192  198  204  210 
245  251  256  262  268 
303  309  315  320  326 

361  367  373  379  384 
419  425  431  437  442 
477  483  489  495  500 

506  512  518  523  529 

535  541  547  552  558 

N. 

L.  0   1   2   3   4 

56789 

P.P. 

lo  56'  =  6960"  S.  4.  68  549  T.  4.  68  574    2°  1'  =  7260"  S.  4.  68  549  T.  4.  68  575 
1  57  =  7020     4.  68  549    4.  68  574    22=  7320     4.  68  548    4.  68  576 
1  58  =  7080     4.  68  549    4.  68  575    23=  7380     4.  68  548    4.  68  576 
1  59  =  7140     4.  68  549    4.  68  575    24=  7440     4.  68  548     4.  68  576 
2   0  =  7200     4.  68  549    4.  68  575    25=  7500     4.  68  548     4.  68  577 

142          GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

56789 

P.  P. 

750 

751 
752 

753 

754 
755 
756 

757 
758 
759 

760 

761 
762 
763 

764 
765 
766 

767 
768 
769 

770 

771 
772 
773 

774 
775 
776 

777 
778 
779 

780 

781 
782 
783 

784 
785 
786 

787 
788 
789 

790 

791 
792 
793 

794 
795 
796 

-  797 
798 
799 

800 

87  506  512  518  523  529 

535  541  547  552  558 

6 

1  0,6 
2  1,2 
3  1,8 
4  2,4 
5  3,0 
6  3,6 
7  4,2 
8  4,8 
9  5,4 

5 

1  0,5 
2  1,0 
3  1,5 
4  2,0 
5  2,5 
6  3,0 
7  3,5 
8  4,0 
9  4,5 

564  570  576  581  587 
622  628  633  639  645 
679  685  691  697  703 

737  743  749  754  760 
795  800  806  812  818 
852  858  864  869  875 

910  915  921  927  933 
967  973  978  984  990 
88  024  030  036  041  047 

593  599  604  610  616 
651  656  662  668  674 
708  714  720  726  731 

766  772  777  783  789 
823  829  835  841  846 
881  887  892  898  904 

938  944  950  955  961 
996  *001  *007  *013  *018 
053  058  064  070  076 

081  087  093  098  104 

110  116  121  127  133 

138  144  150  156  161 
195  201  207  213  218 
252  258  264  270  275 

309  315  321  326  332 
366  372  377  383  389 
423  429  434  440  446 

480  485  491  497  502 
536  542  547  553  559 
593  598  604  610  615 

167  173  17§  184  190 
224  230  235  241  247 
281  287  292  298  304 

338  343  349  355  360 
395  400  406  412  417 
451  457  463  468  474 

508  513  519  625  530 
564  570  576  581  587 
621  627  632  638  643 

649  655  660  666  672 

677  683  689  694  700 

705  711  717  722  728 
762  767  773  779  784 
818  824  829  835  840 

874  880  885  891  897 
930  936  941  947  953 
986  992  997  *003  *009 

89  042  048  053  059  064 
098  104  109  115  120 
154  159  165  170  176 

734  739  745  750  756 
790  795  801  807  812 
846  852  857  863  868 

902  908  913  919  925 
958  964  969  975  981 
*014  *020  *025  *031  *037 

070  076  081  087  092 
126  131  137  143  148 
182  187  193  198  204 

209  215  221  226  232 

237  243  248  254  260 

265  271  276  282  287 
321  326  332  337  343 
376  382-  387  393  398 

432  437  443  448  454 
487  492  498  504  509 
542  548  553  559  564 

597  603  609  614  620 
653  658  664  669  675 
708  713  719  724  730 

293  298  304  310  315 
348  354  360  365  371 
404  409  415  421  426 

459  465  470  476  481 
515  520  526  531  537 
570  575  581  586  592 

625  631  636  642  647 
680  686  691  697  702 
735  741  746  752  757 

763  768  774  779  785 

790  796  801  807  812 

818  823  829  834  840 
873  878  883  889  894 
927  933  938  944  949 

982  988  993  998  #004 
90  037  042  048  053  059 
091  097  102  108  113 

146  151  157  162  168 
200  206  211  217  222 
255  260  266  271  276 

845  851  856  862  867 
900  905  911  916  922 
955  960  966  971  977 

*009  #015  *020  #026  #031 
064  069  075  080  086 
119  124  129  135  140 

173  179  184  189  195 
227  233  238  244  249 
282  287  293  298  304 

309  314  320  .325  331 

336  342  347  352  358 

N. 

L.  0   1    2   3   4 

56789 

P.P. 

2°  5'=  7500"  S.  4.  68  548  T.  4.  68  577    2°  10'=  7800"  S.  4.  68  547  T.  4.  68  578 
2  6  =  7560     4.  68  548    4.  68  577    2  11  =  7860     4.  68  547    4.  68  579 
27  =  7620     4.  68  548    4.  68  577    2  12  =  7920     4.  68  547    4.  68  579 
2  8  =  7680     4.  68  547    4.  68  578    2  13  =  7980    4.  68  547    4.  68  579 
29  =  7740     4.  68  547    4.  68  578    2  14  =  8040     4.  68  546    4.  68  579 

GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


143 


N. 

L.  0   1   2   3   4 

56789 

P.P. 

800 

90  309  314  320  325  331 

336  342  347  352  358 

801 

802 

363  369  374  380  385 
417  423  428  434  439 

390  396  401  407  412 
445  450  455  461  466 

803 

472  477  482  488  493 

499  504  509  515  520 

804 

526  531  536  542  547 

553  558  563  569  574 

805 

580  585  590  596  601 

607  612  617  623  628 

806 

634  639  644  650  655 

660  666  671  677  682 

807 

687  693  698  703  709 

714  720  725  730  736 

808 

741  747  752  757  763 

768  773  779  784  789 

809 

795  800  806  811  816 

822  827  832  838  843 

810 

849  854  859  865  870 

875  881  886  891  897 

811 

902  907  913  918  924 

929  934  940  945  950 

6 

812 

966  961  966  972  977 

982  988  993  998  *004 

1    0,6 

813 

91  009  014  020  025  030 

036  041  046  052  057 

2    1,2 

814 

062  068  073  078  084 

089  094  100  105  110 

3    1,8 
4    2,4 

815 

116  121  126  132  137 

142  148  153  158  164 

5    3,0 

816 

169  174  180  185  190 

196  201  206  212  217 

6    3,6 

817 

222  228  233  238  243 

249  264  269  265  270 

7    4,2 
8    4,8 

818 

275  281  286  291  297 

302  307  312  318  323 

9    6,4 

819 

328  334  339  344  350 

355  360  365  371  376 

820 

381  387  392  397  403 

408  413  418  424  429 

821 

434  440  445  450  455 

461  466  471  477  482 

822 
823 

487  492  498  503  508 
540  545  551  656  561 

614  519  524  529  535 
566  572  577  682  587 

824 
825 
826 

593  598  603  609  614 
645  651  656  661  666 
698  703  709  714  719 

619  624  630  635  640 
672  677  682  687  693 
724  730  735  740  745 

827 
828 
829 

751  756  761  766  772 
803  808  814  819  824 
855  861  866  871  876 

777  782  787  793  798 
829  834  840  845  850 
882  887  892  897  903 

830 

908  913  918  924  929 

934  939  944  950  965 

831 

960  965  971  976  981 

986  991  997  *002  *007 

832 
833 

92  012  018  023  028  033 
065  070  075  080  085 

038  044  049  054  059 
091  096  101  106  111 

1    0,5 
2    1,0 
3    1,5 

834 

117  122  127  132  137 

143  148  153  158  163 

4    2,0 

835 

169  174  179  184  189 

195  200  205  210  215 

5    2,5 

836 

221  226  231  236  241 

247  252  267  262  267 

6    3,0 
7    3,5 

837 

273  278  283  288  293 

298  304  309  314  319 

8    4,0 

838 

324  330  335  340  345 

350  355  361  366  371 

9    4,5 

839 

376  381  387  392  397 

402  407  412  418  423 

840 

428  433  438  443  449 

454  459  464  469  474 

841 

480  485  490  495  500 

605  511  516  521  526 

842 

531  536  542  647  552 

657  562  567  572  578 

843 

583  588  593  598  603 

609  614  619  624  629 

844 

634  639  645  650  655 

660  665  670  675  681 

845 

686  691  696  701  706 

711  716  722  727  732 

846 

737  742  747  752  758 

763  768  773  778  783 

847 

848 

788  793  799  804  809 
840  845  850  855  860 

814  819  824  829  834 
865  870  875  881  886 

849 

891  896  901  906  911 

916  921  927  932  937 

850 

942  947  952  957  962 

967  973  978  983  988 

N. 

L.  0   1   2   3   4 

56789 

P.  P. 

2°  13'  =  7980"  S.  4.  68  547  T.  4.  68  579    2°  18'=8280"  8.  4.  68  546  T.  .  68  581 

2  14  =  8040     4.  68  546    4.  68  579    2  19  =8340     4.  68  546     .  68  581 

2  15  =  8100     4.  68  546    4.  68  580    2  20  =8400     4.  68  64$      68  582 

2  16  =8160     4.  68  546    4.  68  580    2  21  -8460     4.  68  54§     .  68  582 
2  17  =  8220     4.  68  546    4.  68  580    2  22  =8520     4.  68  545     .68  582 

144  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.  0   1   2   3   4 

5 

6789 

P 

P. 

850 

92  942  947  952  957  962 

967  973  978  983  988 

851 
852 

993  998  *003  *008  *013 
93  044  049  054  059  064 

$018  *024  ^029  *034  *039 
069  075  080  085  090 

853 

095  100  105  110  115 

120  125  131  136  141 

854 

146  151  156  161  166 

171  176  181  186  192 

855 

197  202  207  212  217 

222  227  232  237  242 

856 

247  252  258  263  268 

273  278  283  288  293 

6 

857 

298  303  308  313  318 

323  328  334  339  344 

1 

0,6 

858 

349  354  359  364  369 

374 

579  384  389  394 

2 

1/2 

859 

399  404  409  414  420 

425  430  435  440  445 

3 
4 

1,8 
2,4 

860 

450  455  460  465  470 

475  480  485  490  495 

5 

3,0 

861 

500  505  510  515  520 

526  531  536  541  546 

6 
7 

3,6 
4,2 

862 

551  556  561  566  571 

576  « 

)81  586  591  596 

4  8 

863 

601  606  611  616  621 

626  631  636  641  646 

9 

4,o 
5,4 

864 

651  656  661  666  671 

676  682  687  692  697 

865 

702  707  712  717  722 

727 

732  737  742  747 

866 

752  757  762  767  772 

777  782  787  792  797 

867 

802  807  812  817  822 

827  832  837  842  847 

868 

852  857  862  867  872 

877  882  887  892  897 

869 

902  907  912  917  922 

927  932  937  942  947 

870 

952  957  962  967  972 

977  982  987  992  997 

871 

94  002  007  012  017  022 

027  032  037  042  047 

5 

872 

052  057  062  067  072 

077  082  086  091  096 

1 

0,5 

873 

101  106  111  116  121 

126  131  136  141  146 

2 

1/0 

874 

151  156  161  166  171 

176  181  186  191  1% 

3 
4 

1/5 
2,0 

875 

201  206  211  216  221 

226  ' 

231  236  240  245 

5 

2,5 

876 

250  255  260  265  270 

275  280  285  290  295 

6 

3,0 

877 

300  305  310  315  320 

325  330  335  340  345 

7 
g 

3,5 
4,0 

878 

349  354  359  364  369 

374  I 

579  384  389  394 

9 

4,5 

879 

399  404  409  414  419 

424  429  433  438  443 

880 

448  453  458  463  468 

473  478  483  488  493 

881 

498  503  507  512  517 

522  527  532  537  542 

882 

547  552  557  562  567 

571  576  581  586  591 

883 

596  601  606  611  616 

621  626  630  635  640 

884 

645  650  655  660  665 

670  675  680  685  689 

885 

694  699  704  709  714 

719  ' 

724  729  734  738 

886 

'  743  748  753  758  763 

768  773  778  783  787 

4 

887 

792  797  802  807  812 

817  822  827  832  836 

1 

0,4 

•  888 

841  846  851  856  861 

866  871  876  880  885 

2' 

0,8 

889 

890  895  900  905  910 

915  919  924  929  934 

3 

1,2 

890 

939  944  949  954  959 

963  968  973  978  983 

4 
5 

1,6 
2,0 

891 
892 
893 

988  993  998  *002  *007 
95  036  041  046  051  056 
085  090  095  100  105 

#012  *017  *022  *027  *032 
061  066  071,  075  080 
109  114  119  124  129 

6 

7 
8 
9 

2,4 

2,8 
3,2 
3,6 

894 

134  139  143  148  153 

158  ] 

L63  168  173  177 

895 

182  187  192  197  202 

207  ', 

211  216  221  226 

896 

231  236  240  245  250 

255  260  265  270  274 

897 

279  284  289  294  299 

303  308  313  318  323 

898 

328  332  337  342  347 

352 

J57  361  366  371 

899 

376  381  386  390  395 

400  405  410  415  419 

900 

424  429  434  439  444 

448  453  458  463  468 

N. 

L.  0   1   2   3   4 

5 

6789 

P.  P. 

2°  21'  =  8460"  S.  4.  68  545  T.  4.  68  582 

2°  26'  =  8760"  S.  4.  68  544  T  4.  68  584 

2  22  =  8520     4.  68  545    4.  68  582 

2  27  =8820     4.  68544 

4.  68  584 

2  23  =  8580     4.  68  545    4.  68  583 

2  28  =  8880     4.  68  544 

4.  68  584 

2  24  =  8640     4.  68  545    4.  68  583 

2  29  =  8940     4.  68  544 

4.  68  585 

2  25  =  8700     4.  68  545    4.  68  583 

2  30  =  9000     4.  68  544 

4.  68  585 

GEOGKAPH1C    TABLES    AND    FORMULAS. 
TABLE  21. — Five-place  logarithms  of  natural  numbers — Continued. 


145 


X. 

L.  0   1   2   3   4 

56789 

P.  P. 

900 

95  424  429  434  439  444 

448  453  458  463  468 

901 

902 

472  477  482  487  492 
521  525  530  535  540 

497  501  506  511  516 
545  550  554  559  564 

903 

569  574  578  583  588 

593  598  602  607  612 

904 

617  622  626  631  636 

641  646  650  655  660 

905 

665  670  674  679  684 

689  694  698  703  708 

906 

713  718  722  727  732 

737  742  746  751  756" 

907 

761  766  770  775  780 

785  789  794  799  804 

908 

809  813  818  823  828 

832  837  842  847  852 

909 

856  861  866  871  875 

880  885  890  895  899 

910 

904  909  914  918  923 

928  933  938  942  947 

911 

952  957  961  966  971 

976  980  985  990  995 

•  • 

912 
913 

999  *004  *009  *014  #019 
%  047  052  057  061  066 

#023  *028  *033  *038  *042 
071  076  080  085  090 

5 

1  0,5 

2  1,0 

914 

095  099  104  109  114 

118  123  128  133  137 

3  1,5 

915 

142  147  162  156  161 

166  171  175  180  185 

4  2,0 

916 

190  194  199  204  209 

213  218  223  227  232 

5  2,5 

917 

•  237  242  246  251  256 

261  265  270  275  280 

6  3,0 
7  3,5 

918 
919 

284  289  294  298  303 
332  336  341  346  350 

308  313  317  322  327 
355  360  365  369  374 

8  4,0 
9  4,5 

920 

379  384  388  393  398 

402  407  412  417  421 

921 

426  431  435  440  445 

450  454  459  464  468 

922 
923 

473  478  483  487  492 
520  525  530  534  539 

497  501  506  511  515 
544  548  553  558  562 

924 

567  572  577  581  586 

591  595  600  605  609 

925 

614  619  624  628  633 

638  642  647  652  656 

926 

661  666  670  675  680 

685  689  694  699  703 

927 

928 

708  713  717  722  727 
755  759  764  769  774 

731  736  741  745  750 

778  783  788  792  797 

929 

802  806  811  816  820 

825  830  834  839  844 

930 

848  853  858  862  867 

872  876  881  886  890 

931 

895  900  904  909  914 

918  923  928  932  937 

932 

942  946  951  956  960 

965  970  974  979  984 

4 

933 

988  993  997  *002  *007 

,,,011  *016  *021  #025  *030 

1  0,4 

934 

97  035  039  044  (M9  053 

058  063  067  072  077 

2  0,8 

935 

081  086  090  095  100 

104  109  114  118  123 

936 

128  132  137  142  146 

151.  155  160  165  169 

5  2,0 

937 

174  179  183  188  192 

197  202  206  211  216 

6  2,4 

938 

220  225  230  234  239 

243  248  253  257  262 

939 

267  271  276  280  285 

290  294  299  304  308 

9  3,6 

940 

313  317  322  327  331 

336  340  345  350  354 

941 

359  364  368  373  377 

382  387  391  396  400 

942 
943 

405  410  414  419  424 

451  456  460  465  470 

428  433  437  442  447 
474  479  483  488  493 

944 

497  502  506  511  516 

520  525  529  534  539 

945 

543  548  552  557  562 

566  571  575  580  585 

946 

589  594  598  603  607 

612  617  621  626  630 

947 
948 
949 

635  640  644  649  653 
681  685  690  695  699 
727  731  736  740  745 

658  663  667  672  676 
704  708  713  717  722 
749  754  759  763  768 

950 

772  777  782  786  791 

795  800  804  809  813 

X. 

L.  0   1   2   3   4 

56789 

P.  P. 

2°  30'  =  9000"  S.  4.  68  544  T.  4.  68  585    2°  35'  =  9300"  S.  4.  68  543  T.  4.  68  587 

2  31  =  9060     4.  68  544    4.  68  585    2  36  =  9360     4.  68  543    4.  68  587 

2  32  =  9120     4.  68  543    4.  68  586    2  37  =  9420     4.  68  542    4.  68  588 

2  33  =  9180     4.  68  543    4.  68  586    2  38  =  9480     4.  68  542    4.  68  588 

2  34  =  9240     4.  68  643    4.  68  587    2  39  =  9640     4.  68  642    4.  68  588 

46061—08 10 


146          GEOGEAPHIC  TABLES  AND  FOEMULAB. 

TABLE  21.—  Five-place  logarithms  of  natural  numbers — Continued. 


N. 

L.   0   1   2   3   4 

5 

6789 

P.P. 

950 

97  772  777  782  786  791 

795 

300  804  809  813 

951 

818  823  827  832  836 

841  845  850  855  859 

952 
953 

864  868  873  877  882 
909  914  918  923  928 

886  891  896  900  905 
932  937  941  946  950 

954 

955  959  964  968  973 

978  982  987  991  996 

955 
956 

98  000  005  009  014  019 
046  050  055  059  064 

023  028  032  037  041 
068  073  078  082  087 

957 

091  096  100  105  109 

114  118  123  127  132 

958 

137  141  146  150  155 

159 

164  168  173  177 

* 

•  959 

182  186  191  195  200 

204  209  214  218  223 

960 

227  232  236  241  245 

250  254  259  263  268 

961 

272  277  281  286  290 

295 

299  304  308  313 

5 

962 

318  322  327  331  336 

340 

345  349  354  358 

1  0,5 

963 

363  367  372  376  381 

385 

390  394  399  403 

2  1,0 

964 
965 

408  412  417  421  426 
453  457  462  466.  471 

430  435  439  444  448 
475  480  484  489  493 

3  1,5 
4  2,0 
5  2,5 

966 

498  502  607  511  516 

520 

325  529  534  538 

6  3,0 

967 

543  547  552  556  561 

565  570  574  579  583 

7  3,5 
8  4,0 

968 
969 

588  592  597  601  605 
632  637  641  646  650 

610  614  619  623  628 
655  659  664  668  673 

9  4,5 

970 

677  682  686  691  695 

700  704  709  713  717 

971 

722  726  731  735  740 

744  749  753  758  762 

972 

767  771  776  780  784 

789  793  798  802  807 

973 

811  816  820  825  829 

834  838  843  817  851 

974 

856  860  865  869  874 

878 

383  887  892  896 

975 
976 

900  905  909  914  918 
945  949  954  958  963 

923  927  932  936  941 
967  972  976  981  985 

977 
978 

989  994  998  *003  *007 
99  034  038  043  047  052 

*012  #016  *021  *025  *029 
056  061  065  069  074 

979 

078  083  087  092  096 

100  105  109  114  118 

980 

123  127  131  136  140 

145  149  154  158  162 

981 

167  171  176  180  185 

189  193  198  202  207 

4 

982 
983 

211  216  220  224  229 
255  260  264  269  273 

233  238  242  247  251 

277  282  286  291  295 

1  0,4 

2  0,8 

984 

300  304  308  313  317 

322  326  330  335  339 

3  1,2 

985 

344  348  352  357  361 

366  370  374  379  383 

4  1,6 

986 

388  392  396  401  405 

410 

114  419  423  427 

5  2,0 

6  2,4 

987 

988 
989 

432  436  441  445  449 
476  480  484  489  493 
520  624  628  533  537 

454  458  463  467  471 
498  502  506  511  515 
542  546  550  555  559 

7  2,8 
8  3,2 
9  3,6 

990 

564  568  572  577  581 

685  590  594  599  603 

991 

607  612  616  621  625 

629  634  638  642  647 

992 

651  656  660  664  669 

673  677  682  686  691 

993 

695  699  704  708  712 

717  721  726  730  734 

994 

739  743  747  752  756 

760  765  769  774  778 

995 

782  787  791  795  800 

804 

308  813  817  822 

9% 

826  830  835  839  843 

848  852  856  861  865 

997 

870  874  878  883  887 

891  896  900  904  909 

998 

913  917  922  926  930 

935  939  944  948  952 

999 

957  961  965  970  974 

978  983  987  991  996 

1000 

00  000  004  009  013  017 

022  026  030  035  039' 

N. 

L.   0   1   2   3   4 

5 

6789 

P.P. 

2°  38'  —  9480"  S.  4.  68  642  T.  4.  68  588 

2°  43'=  9780"  S.  4.  68  541  T.  4.  68  590 

2  39  -  9540     4.  68  642    4.  68  588 

2  44  =  9840    4.  68  641    4.  68  590 

2  40  =  9600     4.  68  542    4.  68  589 

2  45  =  9900    4.  68  541    4.  68  591 

2  41  =  9660     4.  68  542    4.  68  589 

2  46  =  9960    4.  68  541    4.  68  591 

2  42  =9720     4.  68  541    4.  68  590 

2  47  =10020    4.  68  540    4.  68  592 

GEOGRAPHIC  TABLES  AND  FORMULAS.          147 


Formula  for  using  quantities  S  and  T: 
log  sin  a  =  log  a"  +  S. 

log  tan  a  =          log  a"  +  T. 
log  cot  a  =  a.  c.  log  a"  -fa.  c.  log  7! 

log  a"  =  log  sin  a  —  S  =  log  tan  #  —  T7. 

log  cos  a  =  log  (90°  -  a)"  +  A 
log  cot  a  =  log  (90°  -  <*)"  +  T7. 
log  tan  a  =  a.  c.  log  (90°  -  a}"  +  a.  c.  log  T. 

log  (90°  —  a)"  =  log  cos  a—  8=  log  cot  a  —  T. 


148  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  expressed  in  arc  and  time. 

Oh  0° 


m.  s. 

' 

L.  Sin. 

d. 

L.  T'ang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

0   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

6.  46  373 
6.  76  476 
6.94  085 
7.  06  579 

30103 
17609 
12494 
9691 

6.  46  373 
6.  76  476 

6.  94  085 
7.  06  579 

30103 
17609 
12494 
9691 

3.  53  627 
3.  23  524 
3.  05  915 
2.  93  421 

0.00  000 
0.00  000 
0.00  000 
0.00  000 
0.  00  000 

60 

59 
58 
57 
56 

60   0 
56 
52 
48 
44 

0  20 
24 

28 
32 
36 

5 
6 

7 
8 
9 

7.  16  270 
7.24  188 
7.  30  882 
7.36  682 
7.41  797 

7918 
6694 
5800 
5115 
4576 

7.  16  270 
7.  24  188 
7.  30  882 
7.  36  682 
7.41  T97 

7918 
6694 
5800 
5115 
4576 

2.83  730 
2.  75  812 
2.69  118 
2.  63  318 
2.  58  203 

0.00  000 
0.00  000 
0.00  000 
0.00  000 
0.00  000 

55 
54 
53 
52 
51 

59  40 
36 
32 
28 
24 

0  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

7.  46  373 
7.  50  512 
7.  54  291 
7.57  767 
7.  60  985 

4139 
3779 
3476 
3218 
2997 

7.46  373 
7.  50  512 
7.54  291 

7.57  767 
7.  60  986 

4139 
3779 
3476 
3219 
2996 

2.  53  627 
2.  49  488 
2.  45  709 
2.  42  233 
2.  39  014 

0.00  000 
0.00  000 
0.00  000 
0.00  000 
0.00  000 

50 

49 
48 
47 
46 

59  20 
16 
12 
8 
4 

1   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

7.  63  982 
7.66  784 
7.  69  417 
7.71  900 
7.  74  248 

2802 
2633 
2483 
2348 

2227 

7.63  982 
7.66  785 
7.69  418 
7.71  900 
7.  74  248 

2803 
2633 
2482 
2348 

2228 

2.  36  018 
2.33  215 
2.  30  582 
2.  28  100 
2.  25  752 

0.00  000 
0.00  000 
9.  99  999 
9.99  999 
9.  99  999 

45 
44 
43 
22 
41 

59   0 
56 
52 
48 
44 

1  20 
24 

28 
32 
36 

20 

21 
22 
23 
24 

7.  76  475 
7.  78  594 
7.80  615 
7.  82  545  ' 
7.84  393 

2119 
2021 
1930 
1848 

7.76  476 
7.  78  595 
7.  80  615 
7.82  546 
7.  84  394 

2119 
2020 
1931 

1848 
1773 

2.  23  524 
2.  21  405 
2.  19  385 
2.17  454 
2.  15  606 

9.  99  999 
9.  99  999 
9.  99  999 
9.99  999 
9.99  999 

40 

39 
38 
37 
36 

58  40 
36 
32 
28 
24 

1  40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

7.  86  166 

7.87  870 
7.  89  509 
7.91  088 
7.92  612 

1704 
1639 
1579 
1524 
14721 

7.  86  167 
7.  87  871 
7.  89  510 
7.91  089 
7.  92  613 

1704 
1639 
1579 
1524 
1473 

2.  13  833 
2.  12  129 
2.  10  490 
2.  08  911 
2.  07  387 

9.  99  999 
9.99  999 
9.  99  999 
9.  99  999 
9.  99  998 

35 
34 
33 
32 
31 

58  20 
16 
12 
8 
4 

2   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

7.  94  084 
7.  95  508 
7.%  887 
7.  98  223 
7.99  520 

1424 
1379 
1336 
1297 
IOCQ 

7.  94  086 
7.  95  510 
7.  96  889 
7.  98  225 
7.  99  522 

1424 
1379 
1336 
1297 

2.  05  914 
2.  04  490 
2.03  111 
2.01  775 
2.  00  478 

9.  99  998 
9.  99  998 
9.  99  998 
9.  99  998 
9.  99  998 

30 

29 
28 
27 
26 

58   0 
56  . 
52 
48 
44 

2  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

8.  00  779 
8.  02  002 
8.03  192 
8.  04  350 
8.  05  478 

1223 
1190 
1158 
1128 

8.  00  781 
8.02  004 
8.03  194 
8.04  353 
8.  05  481 

1223 
1190 
1159 
1128 

1.  99  219 
1.  97  996 
1.  96  806 
1.95  647 
1.  94  519 

9.  99  998 
9.  99  998 
9.  99  997 
9.  99  997 
9.  99  997 

25 
24 
23 
22 
21 

57  40 
36 
32 
28 
24 

2  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

8.  06  578 
8.07  650 
8.  08  696 
8.09  718 
8.10  717 

1072 
1046 
1022 
999 

8.  06  581 
8.  07  653 
8.  08  700 
8.09  722 
8.  10  720 

1072 
1047 
1022 

998 

1.  93  419 
1.  92  347 
1.91  300 
1.90  278 
1.89  280 

9.  99  997 
9.  99  997 
9.  99  997 
9.  99  997 
9.  99  996 

20 

19 
18 
17 
16 

57  20 
16 
12 
8 
4 

3   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

8.  11  693 
8.  12  647 
8.  13  581 
8.  14  495 
8.  15  391 

954 
934 
914 
896 

8.11  696 
8.  12  651 
3.13  585 
8.  14  500 
8.  15  395 

955 
934 
915 
895 

1.88  304 
1.  87  349 
1.  86  415 
1.  85  500 
1.84  605 

9.99  996 
9.  99  996 
9.  99  996 
9.  99  996 
9.99  9% 

15 
14 
13 
12 
11 

57   0 

56 
52 
48 
44 

3  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

3.  16  268 
8.17  128 
8.17  971 
8.  18  798 
8.  19  610 

860 
843 
827 
812 
7Q7 

8.  16  273 
8.  17  133 
8.  17  976 
8.  18  804 
8.19  616 

860 

•843 
828 
812 

1.83  727 
1.  82  867 
1.82  024 
1.81  196 
1.  80  384 

9.  99  995 
9.  99  99§ 
9.99  995 
9.  99  995 
9.99  995 

10 

9 

8 
7 
6 

56  40 
36 
32 
28 
24 

3  40 

44 
48 
52 
56 

55 
56 
57 
58 
59 

8.  20  407 
8.21  189 
8.21  958 
8.22  713 
8.  23  456 

782 
769 
755 
743 

70n 

8.  20  413 
8.21  195 
8.21  964 
8.22  720 
8.  23  462 

782 
769 
756 
742 

1.  79  587 
1.  78  805 
1.78  036 
1.77  280 
1.  76  538 

9.  99  994 
9.  99  994 
9.  99  994 
9.  99  994 
9.  99  994 

5 
4 
3 
2 
1 

56  20 
16 
12 
8 
4 

4   0 

60 

8.  24  186 

8.  24  192 

1.75  808 

9  99  993 

0 

56   0 

L.  Cos. 

d. 

|L.  Cotg. 

C.  d. 

L.  Tang. 

L.  Sin. 

' 

m.  s. 

89 


GEOGRAPHIC    TABLES    AND    FORMULAS.  149 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 


m.   s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

4   0 
4 

8 
12 
16 

0 

1 
2 
3 

4 

8.  24  186 
8.  24  903 
8.  25  609 
8.26  304 
8.  26  988 

717 
706 
695 

684 

8.24  192 
8.  24  910 
8.  25  616 
8.  26  312 
8.26  996 

718 
706 
696 
684 

1.75  808 
1.75  090 
1.  74  384 
1.73  688 
1.73  004 

9.  99  993 
9.  99  993 
9.  99  993 
9.99  993 
9.  99  992 

60 

59 
58 
57 
56 

56   0 
56 
52 
48 
44 

4   20 

24 
28 
32 
36 

5 
6 

8 
9 

8.27  661 
8.28  324 
8.  28  977 
8.29  621 
8.30  255 

663 
653 
644 
634 

8.27  669 
8.28  332 
8.  28  986 
8.29  629 
8.  30  263 

663 
654 
643 
634 

1.  72  331 
1.  71  668 
1.71  014 
1.  70  371 
1.  69  737 

9.  99  992 
9.  99  992 
9.  99  992 
9.  99  992 
9.  99  991 

55 
54 
53 
52 
51 

55   40 
36 
32 

28 
24 

4   40 
44 
48 
52 
M 

10 

11 
12 
13 
14 

8.  30  879 
8.  31  495 
8.  32  103 
8.32  702 
8.33  292 

616 

608 
599 
590 

8.30  888 
8.31  505 
8.32  112 
8.  32  711 
8.  33  302 

617 
607 
599 
591 

1.  69  112 

1.  68  495 
1.67  888 
1.  67  289 
1.  66  698 

9.99  991 
9.  99  991 
9.  99  990 
9.99  990 
9.99  990 

50 

49 
48 
47 
46 

55   20 
16 
12 

8 
4 

5   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

8.  33  875 
8.  34  450 
8.  35  018 
8.  35  578 
8.  36  131 

575 

568 
560 
553 

8.33  886 
8.  34  461 
8.35  029 
8.35  590 
8.  36  143 

575 
568 
561 
553 

1.66  114 
1.  65  539 
1.64  971 
1.  64  410 
1.  63  857 

9.99  990 
9.  99  989 
9.99  989 
9.  99  989 
9.  99  989 

45- 
44 
43 
42 
41 

55   0 

56 
52 
48 
44 

5   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

8.36  678 
8.  37  217 
8.  37  750 
8.38  276 
8.  38  796 

539 
533 
526 
520 

8.36  689 
8.  37  229 
8.37  762 
8.38289 
8.38  809 

540 
533 
527 
520 

1.  63  311 
1.62  771 
1.62  238 
1.61  711 
1.61  191 

9.  99  988 
9.99  988 
9.99  9S8 
9.  99  987 
9.  99  987 

40 

39 
38 
37 
36 

54   40 
36 
32 
28 
24 

5   40 
44 

48 
52 
56 

25 
26 

27 
28 
29 

8.  39  310 
8.  39  818 
8.  40  320 
8.  40  816 
8.41  307 

508 
502 
496 
491 

8.  39  323 
8.  39  832 
8.  40  334 
8.  40  830 

s.  11  u-jl 

509 
502 
496 
491 

1.  60  677 
1.60  168 
1.  59  666 
1.59  170 
1.58  679 

9.  99  987 
9.99  986 
9.  99  986 
9.  99  986 
9.  99  985 

35 
34 
33 
32 
31 

54   20 
16 
12 
8 
4 

6   0 
4 

8 
12 

10 

30 

31 
32 
33 
34 

8.41  792 
8.  42  272 
8.  42  746 
8.  43  216 
8.43  680 

480 
474 
470 
464 

S.-ll  W)7 
8.  42  287 
8.  42  762 
8.  43  232 
8.  43  6% 

480 
475 
47.0 
464 

1,58  193 
1.57  713 
1.57  238 
1.56  768 
1.56  304 

9.  99  985 
9.99  985 
9.  99  984 
9.  99  984 
9.  99  984 

30 

29 
28 
27 
26 

54   0 

56 
52 
48 
44 

6   20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

8.  44  139 
8.  44  594 
8.  45  044 
8.  45  489 
8.45930 

455 
450 
445 
441 

8.  44  156 
8.  44  611 
8.  45  061 
8.  45  507 
8.45  948 

455 
450 
446 
441 

1.55  844 
1.55  389 
1.54  939 
1.  54  493 
1.54  052 

9.  99  983 
9.  99  983 
9.  99  983 
9.  99  982 
9.  99  982 

25 
24 
23 
22 
21 

53   40 
36 
32 
28 
24 

6   40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

8.46  366 
8.46  799 
8.47  226 
8.47  650 
8.  48  069 

433 
427 
424 
419 

8.46  385 
8.  46  817 
8.  47  245 
8.  47  669 
8.  48  089 

432 

428 
424 
420 

1.53  615 
1.  53  183 
1.52  755 
1.  52  331 
1.51  911 

9.  99  982 
9.  99  981 
9.  99  981 
9.  99  981 
9.  99  980 

20 

19 
18 
17 
16 

53   20 
16 
12 
8 
4 

7   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

8.  48  485 
8.  48  896 
8.  49  304 
8.49  708 
8.50  108 

411 

408 
404 
400 

8.48  505 
8.48  91? 
8.  49  325 
8.  49  729 
8.  50  130 

412 
408 
404 
401 

1.51  495 
1.51  083 
1.50  675 
1.50  271 
1.  49  870 

9.  99  980 
9.  99  979 
9.  99  979 
9.99  979 
9.  99  978 

15 
14 
13 
12 
11 

53   0 

56 
52 
48 
44 

7   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

8.50  504 
8.  50  897 
8.51  287 
8.51  673 
8.52  055 

393 
390 
386 

382 

8.  50  527 
8.50  920 
8.51  310 
8.51  6% 
8.  52  079 

393 
390 
386 
383 

1.  49  473 
1.49  080 
1.48  690 
1.48  304 
1.  47  921 

9.  99  978 
9.  99  977 
9.  99  977 
9.  99  977 
9.  99  976 

10 
9 

8 
7 
6 

52   40 
36 
32 

28 
24 

7   40 
44 
48 
62 
56 

55 
56 
57 

58 
f,'J 

8.  52  434 
8.  52  810 
8.53  183 
8.53  552 
8.  53  919 

376 
373 
369 
367 

8.  52  459 
8.52  835 
8.  53  208 
8.53  5^8 
8.  53  945 

376 
373 
370 
367 

1.47  541 
1.47  165 
1.46  792 
1.46  422 
1.  46  055 

9.  99  976 
9.  99  975 
9.  99  975 
9.  99  974 
9.  99  974 

5 
4 
3 
2 
1 

52   20 
16 
12 
8 
4 

8   0 

60 

8.54  282 

8.54  308 

1.45  692 

9.  99  974 

0 

52   0 

L.Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

i 

m.  s. 

88 


5h 


150  GEOGRAPHIC    TABLES    AND    FOEMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

Oh  2° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

8   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

8.  54  282 
8.54  642 
8.  54  999 
8.55  354 
8.55  705 

360 
357 
355 
351 
040 

8.54  308 
8.  54  669 
8.  55  027 
8.  55  382 
8.  55  734 

361 

358 
355 
352 
040 

1.  45  692 
1.  45  331 
1.44  973 
1.  44  618 
1.  44  266 

9.99  974 
9.  99  973 
9.  99  973 
9.  99  972 
9.  99  972 

60 

59 

58 
57 
56 

52   0 
56 
52 
48 
44 

8  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

8.  56  054 
8.  56  400 
8.  56  743 
8.  57  084 
8.  57  421 

346 
343 
341 
337 

qoc 

8.  56  083 
8.  56  429 
8.56  773 
8.57  114 
8.  57  452 

346 
344 
341 

338 

OOfi 

1.43  917 
1.43  571 
1.  43  227 
1.  42  886 
1.42  548 

9.  99  971 
9.  99  971 
9.  99  970 
9.  99  970 
9.  99  969 

55 
54 
53 
52 
51 

51  40 
36 
32 

28 
24 

8  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

8.57  757 
8.  58  089 
8.58  419 
8.  58  747 
8.  59  072 

332 
330 
328 
325 

000 

8.57  788 
8.58  121 
8.  58  451 
8.  58  779 
8.59  105 

333 
380 
328 
326 

000 

1.42  212 
1.41  879 
1.41  549 
1.  41  221 
1.  40  895 

9.  99  969 
9.  99  968 
9.  99  968 
9.  99  967 
9.  99  967 

50 

49 
48 
47 
46 

51  20 
16 
12 
8 
4 

9   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

8.  59  395 
8.  59  715 
8.  60  033 
8.60  349 
8.  60  662 

320 
318 
316 
313 

8.  59  428 
8.  59  749 
8.  60  068 
8.60  384 
8.  60  698 

321 
319 
316 
314 

1.  40  572 
1.  40  251 
1.  39  932 
1.  39  616 
1.  39  302 

9.  99  967 
9.  99  966 
9.  99  966 
9.  99  965 
9.  99  964 

45 
44 
43 
42 
41 

51   0 
56 
52 
48 
44 

9  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

8.  60  973 
8.61  282 
8.  61  589 
8.61  894 
8.  62  196 

309 
307 
305 
302 

8.  61  009 
8.61  319 
8.  61  626 
8.61  931 
8.  62  234 

310 
307 
305 
303 

1.  38  991 
1.  38  681 
1.38  374 
1.  38  069 
1.37  766 

9.  99  964 
9.  99  963 
9.  99  963 
9.  99  962 
9.  99  962 

40 

39 
38 
37 
36 

50  40 
36 
32 
28 
24 

9  40 
44 
48 
52 
56 

25 
26 

27 
28 
29 

8.  62  497 
8.  62  795 
8.  63  091 
8.63  385 
8.  63  678 

298 
296 
294 
293 
290 

8.  62  535 
8.  62  834 
8.  63  131 
8.  63  426 
8.  63  718 

299 

297 
295 
292 
291 

1.  37  465 
1.  37  166 
1.  36  869 
1.36  574 
1.  36  282 

9.  99  961 
9.  99  961 
9.  99  960 
9.  99  960 
9.  99  959 

35 
34 
33 
32 
31 

50  20 
16 

12 

8 
4 

10   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

8.  63  968 
8.  64  256 
8.  64  543 
8.  64  827 
8.  65  110 

288 
287 
284 
283 

001 

8.  64  009 
8.  64  298 
8.64  585 
8.  64  870 
8.  65  154 

289 

287 
285 
284 

001 

1.  35  991 
1.  35  702 
1.  35  415 
1.35  130 
1.  34  846 

9.  99  959 
9.  99  958 
9.99  958 
9.  99  957 
9.  99  956 

30 

29 
28 
27 
26 

50   0 
56 
52 
48 
44 

10  20 
24 
28 
32 
36 

35 

36 
37 
38 
39 

8.  65  391 
8.  65  670 
8.  65  947 
8.  66  223 
8.  66  497 

279 

277 
276 
274 
272 

8.  65  4&5 
8.65  715 
8.  65  993 
8.  66  269 
8.  66  543 

280 
278 
276 
274 
273 

1.34  565 
1.34  285 
1.  34  007 
1.  33  731 
1.33  457 

9.  99  956 
9.  99  955 
9.  99  955 
9.  99  954 
9.  99  954 

25 
24 
23 
22 
21 

49  40 
36 
32 

28 
24 

10  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

8.  66  769 
8.  67  039 
8.  67  308 
8.  67  575 
8.  67  841 

270 
269 
267 
266 
263 

8.  66  816 
8.  67  087 
8.  67  356 
8.  67  624 
8.  67  890 

271 
269 
268 
266 
264 

1.33  184 
1.  32  913 
1.  32  644 
1.  32  376 
1.  32  110 

9.  99  953 
9.  99  952 
9.  99  952 
9.  99  951 
9.  99  951 

20 

19 
18 
17 
16 

49  20 
16 
12 

8 
4 

11  0 

4 
8 
12 
16 

45 

46 
47 
48 
49 

8.  68  104 
8.  68  367 
8.  68  627 
8.  68  886 
8.  69  144 

263 

260 
259 
258 
256 

8.  68  154 
8.  68  417 
8.  68  678 
8.  68  938 
8.  69  196 

263 
261 
260 
258 
257 

1.31  846 
1.31  583 
1.  31  322 
1.31  062 
1.30804 

9.  99  950 
9.  99  949 
9.  99  949 
9.  99  948 
9.  99  948 

15 
14 
13 
12 
11 

49   0 
56 
52 
48 
44 

11  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

8.  69  400 
8.  69  654 
8.  69  907 
8.  70  159 
8.  70  409 

254 
253 
252 
250 
249 

8.  69  453 
8.  69  708 
8.  69  962 
8.  70  214 
8.  70  465 

255 

254 
252 
251 
249 

1.30  547 
1.30  292 
1.30  038 
1.  29  786 
1.  29  535 

9.  99  947 
9.  99  946 
9.  99  946 
9.  99  945 
9.  99  944 

10 

9 

8 
7 
6 

48  40 
36 
32 
28 
24 

11  40 
44 
48 
52 
56 

55 
56 
57 
68 
59 

8.  70  658 
8.70  905 
8.71  151 
8.71  395 
8.  71  638 

247 
246 
244 
243 
242 

8.  70  714 

8.  70  962 
8.  71  208 
8.  71  453 
8.71  697 

248 
246 
245 
244 
243 

1.29  286 
1.29  038 
1.28  792 
1.  28  547 
1.  28  303 

9.  99  944 
9.  99  943 
9.  99  942 
9.  99  942 
9.99  941 

5 
4 
3 
2 
1 

48  20 
16 
12 
8 
4 

12   0 

60 

8.71  880 

8.  71  940 

1.28  060 

9.  99  940 

0 

48   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.Tang. 

L.  Sin. 

/ 

m.  s. 

87° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  151 

TABLE  22. — five-place  logarithms  of  circular  functions,  etc. — Continued. 
0*  3° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

12   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

8.71  880 
8.  72  120 
8.  72  359 
8.  72  597 
8.72  834 

240 
239 
238 
237 

8.71  940 
8.  72  181 
8.  72  420 
8.  72  659 
.  8.  72  896 

241 
239 
239 
237 

1.  28  060 
1.27  819 
1.27  580 
1.  27  341 
1.27  104 

9.99  940 
9.  99  940 
9.  99  939 
9.  99  938 
9.  99  938 

60 

59 
58 
57 
56 

48   0 
56 
52 
48 
44 

12   20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

8.  73  069 
8.  73  303 
8.73  535 
8.  73  767 
8.  73  997 

234 
232 
232 
230 

8.  73  132 

8.  73  366 
8.73  600 
8.  73  832 
8.  74  063 

234 

234 
232 
231 

1.26  868 
1.26634 
1.  26  400 
1.  26  168 
1.  25  937 

9.  99  937 
9.  99  936 
9.  99  936 
9.  99  935 
9.  99  934 

55 
54 
53 
52 
51 

47  40 
36 
.  32 
28 
24 

12   40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

8.  74  226 
8.  74  454 

8.74  680 
8.74  906 
8.75  130 

228 
226 
226 
224 

8.  74  292 
8.  74  521 
8.  74  748 
8.  74  974 
8.  75  199 

229 
227 
226 
225 

1.  25  708 
1.25  479 
1.  25  252 
1.25  026 
1.  24  801 

9.99  934 
9.  99  933 
9.  99  932 
9.  99  932 
9.  99  931 

50 

49 
48 
47 
46 

47  20 
16 
12 
8 
4 

13   0 
4 
8 
12 
16 

15 
16 
17 

18 
19 

8.75  353 
8.  75  575 
8.  75  795 
8.  76  015 
8.76  234 

222 
220 
220 
219 

8.  75  423 

8.  75  645 
8.  75  867 
8.  76  087 
8.76  306 

222 
222 
220 
219 

1.  24  577 
1.24  355 
1.  24  133 
1.  23  913 
1.23  694 

9.  99  930 
9.  99  929 
9.99  929 
9.99  928 
9.  99  927 

45 
44 
43 
42 
41 

47   0 

56 
52 

48 
44 

13   20 
24 
28 
32 
36 

20 

21 
22 
23 

24 

8.  76  451 
8.  76  667 
8.76  883 
8.  77  097 
8.77  310 

216 
216 
214 
213 

8.  76  525 
8.  76  742 
8.  76  958 

8.  77  173 
8.  77  387 

217 
216 
215 
214 

1.23  475 
1.23258 
1.23  042 
1.22  827 
1.  22  613 

9.  99  926 
9.  99  926 
9.  99  925 
9.99  924 
9.99  923 

40 

39 
38 
37 
36 

46  40 
36 
32 
28 
24 

13   40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

8.  77  522 
8.  77  733 
8.  77  943 
8.  78  152 
8.78  360 

211 
210 
209 
208 

8.77600 
8.  77  811 
8.  78  022 
8.  78  232 
8.  78  441 

211 
211 
210 
209 

ono 

1.  22  400 
1.  22  189 
1.21  978 
1.21  768 
1.  21  559 

9.  99  923 
9.99  922 
9.99  921 
9.99  920 
9.99  920 

35 
34 
33 
32 
31 

46  20 
16 
12 

8 
4 

14   0 
4 

8 
12 
16 

30 

31 
32 
33 
34 

8.78  568 
8.  78  774 
8.  78  979 
8.79  183 
8.79  386 

206 
205 
204 
203 

8.  78  649 
8.  78  855 
8.  79  061 
8.  79  266 
8.  79  470 

206 
206 
205 
204 

1.21  351 
1.21  145 
1.20  939 
1.20  734 
1.20  530 

9.99  919 
9.  99  918 
9.  99  917 
9.  99  917 
9.  99  916 

30 

29 
28 
27 
26 

46   0 
56 
52 

48 
44 

14   20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

8.79  588 
8.  79  789 
8.79  990 
'  8.80  189 
8.80  388 

201 
201 
199 
199 

8.  79  673 

8.  79  875 
8.  80  076 
8.  80  277 
8.  80  476 

202 
201 
201 
199 

1.20327 
1.20  125 
1.  19  924 
1.  19  723 
1.19  524 

9.  99  915 
9.  99  914 
9.  99  913 
9.  99  913 
9.  94  912 

25 
24 
23 

22 
21 

45  40 
36 
32 
28 
24 

14   40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

8.80  585 
8.  80  782 
8.  80  978 
8.81  173 
8.81  367 

197 
196 
195 
194 

8.  80  674 
8.80872 
8.81  068 
8.81  264 
8.81  459 

198 
196 
196 
195 

1.  19  326 
1.  19  128 
1.  18  932 
1.  18  736 
1.18  541 

9.  99  911 
9.  99  910 
9.99  909 
9.99  909 
9.  99  908 

20 

19 
18 
17 
16 

45,20 
16 
12 
8 
4 

15   0 
4 

8 
12 
16 

45 
46 
47 
48 
49 

8.81  560 
8.81  752 
8.  81  944 
8.82  134 
8.  82  324 

192 
192 
190 
190 

8.81  653 
8.81  846 
8.  82  038 
8.  82  230 
8.  82  420 

193 
192 
192 
190 

1.  18  347 
1.  18  154 
1.  17  962 
1.  17  770 
1.  17  580 

9.99  907 
9.99  906 
9.99  905 
9.  99  904 
9.99  904 

15 
14 
13 
12 
11 

45   0 
56 
52 
48 
44 

15   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

8.  82  513 
8.  82  701 
8.82  888 
8.  83  075 
8.83  261 

188 
187 
187 
186 

8.  82  610 
8.  82  799 
8.82  987 
8.83  175 
8.83  361 

189 
188 
188 
186 

1.  17  390 
1.  17  201 
1.  17  013 
1.  16  825 
1.  16  639 

9.  99  903 
9.99  902 
9.  99  901 
9.  99  900 
9.  99  899 

10 

9 

8 
7 
6 

44  40 
36 
32 
28 
24 

15   40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

8.  83  446 
8.83  630 
8.  83  813 

8.83  9% 
8.84  177 

184 
183 
183 
181 

8.83  547 
8.83  732 
8.  83  916 
8.84  100 
8.84  282 

185 
.184 
184 
182 

1.  16  453 
1.16  268 
1.  16  084 
1.15  900 
1.  15  718 

9.  99  898 
9.  99  898 
9.  99  897 
9.  99  896 
9.  99  895 

5 
4 
3 
2 
1 

44  20 
16 
12 

8 
4 

16   0 

60 

8.84  358 

8.84  464 

1.  15  636 

9.  99  894 

0 

44   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

/ 

m.  s. 

152  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  4° 


m.  s. 

> 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

16   0 
4 
8 
12 
16 

0 

1 

2 
3 
4 

8.84  358 
8.  84  539 
8.84  718 
8.  84  897 
8.85  075 

181 
179 
179 
178 
177 

177 
176 
175 
175 
173 

8.84464 
8.84  646 
8.  84  826 
8.85  006 
8.85  185 

182 
180 
180 
179 
178 

177 
177 
176 
176 
174 

174 
174 
172 
172 
171 

171 
170 
169 
169 
168 

167 
167 
166 
165 
165 

165 
163 
163 
163 
161 

162 
160 
160 
160 
159 

158 
158 
157 
157 
156 

155 
155 
155 
153 
154 

153 
152 
152 
151 
151 

150 
150 
149 
148 
149 

147 
147 
147 
146 
146 

1.  15  536 
1.  15  354 
1.15  174 
1.  14  994 
1.  14  815 

9.  99  894 
9.  99  893 
9.  99  892 
9.  99  891 
9.  99  891 

60 

59 

58 
57 
56 

44   0 
56 
52 
48 
44 

16  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

8.85  252 
8.  85  429 
8.  85  605 
8.  85  780 
8.  85  955 

8.  85  363 
8.85  540 
8.  85  717 
8.  85  893 
8.  86  069 

1.  14  637 
1.  14  460 
1.  14  283 
1.  14  107 
1.  13  931 

9.  99  890 
9.  99  889 
9.  99  888 
9.  99  887 
9.  99  886 

55 
54 
53 
52 
51 

43  40 
36 
32 
28 
24 

16  40 

44 
48 
52 
56 

10 

11 
12 
13 
14 

8.  86  128 
8.86  301 
8.  86  474 
8.86  645 
8.  86  816 

173 
173 
171 
171 
171 

169 
169 
169 
167 
168 

166 
166 
165 
164 
164 

8.  86  243 
8.  86  417 
8.86  591 
8.  86  763 
8.  86  935 

1.  13  757 
1.  13  583 
1.  13  409 
1.  13  237 
1.13  065 

9.99  885 
9.  99  884 
9.  99  883 
9.  99  882 
9.  99  881 

50 

49 
48 
47 
46 

43  20 
16 
12 

8 
4 

17   0 
4 
8 
12 
16 

]5 
16 
17 
18 
19 

8.  86  987 
8.  87  156 
8.  87  325 
8.  87  494 
8.  87  661 

8.87  106 
8.87  277 
8.  87  447 
8.87  616 
8.87  785 

1.  12  894 
1.  12  723 
1.12  553 
1.  12  384 
1.  12  215 

9.  99  880 
9.  99  879 
9.  99  879 
9.  99  878 
9.99  877 

45 
44 
43 
42 
41 

43   0 
56 
52 
48 
44 

17  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

8.  87  829 
8.  87  995 
8.88  161 
8.  88  326 
8.88  490 

8.87  953 
8.88  120 
8.88  287 
8.88  453 
8.  88  618 

1.  12  047 
1.  11  880 
1.11  713 
1.  11  547 
1.  11  382 

9.  99  876 
9.  99  875 
9.  99  874 
9.  99  873 
9.  99  872 

40 

39 
38 
37 
36 

35 
34 
33 
32 
31 

42  40 
36 
32 
28 
24 

17  40 
44 

48 
52 
56 

25 
26 
27 
28 
29 

8.88  654 
8.  88  817 
8.  88  980 
8.89  142 
8.  89  304 

163 
163 
162 
162 
160 

8.  88  783 
8.  88  948 
8.  89  111 
8.  89  274 
8.  89  437 

1.  11  217 
1.  11  052 
1.  10  889 
1.  10  726 
1.  10  563 

9.  99  871 
9.99  870 
9.  99  869 
9.  99  868 
9.  99  867 

42  20 
16 
12 

8 
4 

18   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

8.  89  464 
8.  89  625 
8.89  784 
8.89  943 
8.  90  102 

161 
159 
150 
159 

158 

8.  89  598 
8.  89  760 
8.  89  920 
8.  90  080 
8.90  240 

1.  10  402 
1.10  240 
1.  10  080 
1.  09  920 
1.  09  760 

9.  99  866 
9.  99  865 
9.  99  864 
9.  99  863 
9.  99  862 

30 

29 
28 
27 
26 

42   0 
56 
52 
48 
44 

18  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

8.90  260 
8.  90  417 
8.  90  574 
8.90  730 
8.90  885 

157 
157 
156 
155 
155 

155 
154 
153 
153 
152 

152 
151 
151 
150 
150 

149 
149 
148 
147 
147 

147 
146 
146 
145 
145 

8.  90  399 
8.  90  557 
8.  90  715 
8.  90  872 
8.91  029 

1.09  601 
1.  09  443 
1.  09  285 
1.09  128 
1.  08  971 

9.  99  861 
9.  99  860 
9.  99  859 
9.  99  858 
9.  99  857 

25 
24 
23 
22 
21 

41  40 
36 
32 

28 
24 

18  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

8.  91  040 
8.91  195 
8.91  349 
8.91  502 
8.91  655 

8.91  185 
8.  91  340 
8.91  495 
8.91  650 
8.91  803 

1.  08  815 
1.08  660 
1.08  505 
1.  08  350 
1.  08  .197 

9.99  856 
9.  99  855 
9.99  854 
9.  99  853 
9.  99  852 

20 

19 
18 
17 
16 

41  20 
16 
12 

8 
4 

19   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

8.91  807 
8.91  959 
8.92  110 
8.92  261 
8.92  411 

8.91  957 
8.  92  110 
8.  92  262 
8.  92  414 
8.92  565 

1.  08  043 
1.  07  890 
1.  07  738 
1.  07  586 
1.  07  4a5 

9.99  851 
9.  99  850 
9.  99  848 
9.  99  847 
9.  99  846 

15 
14 
13 
12 
11 

41   0 

56 
52 
48 
44 

19  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

8.92  561 
8.92  710 
8.  92  859 
8.  93  007 
8.93  154 

8.92  716 
8.  92  866 
8.93  016 
8.  93  165 
8.  93  313 

1.  07  284 
1.07  134 
1.06  984 
1.06  835 
1.06  687 

9.  99  845 
9,99  844 
9.99  843 
9.  99  842 
9.99841 

10 

9 

8 
7 
6 

40  40 
36 
32 
28 
24 

19  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

8.  93  301 
8.  93  448 
8.  93  594 
8.  93  740 
8.93  885 

8.  93  462 
8.  93  609 
8.  93  756 
8.  93  908 
8.  94  049 

1.06  538 
1.  06  391 
1.06  244 
1.  06  097 
1.  05  951 

9.  99  840 
9.99  839 
9.  99  838 
9.  99  837 
9.99  836 

5 

4 
3 
2 
1 

40  20 
16 
12 

8 
4 

20   0 

60 

8.94  030 

8.94  195 

1.  05  805 

9.99  834 

0 

40   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

i 

m.  s. 

85C 


5h 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


153 


TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

Oh  5° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

20   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

8.94  030 
8.  94  174 
8.  94  317 
8.  94  461 
8.94  603 

144 

143 
144 
142 
143 

8.  94  195 
8.  94  340 
8.94485 
8.  94  630 
8.  94  773 

145 
145 
145 
143 
144 

1.05  805 
1.05  660 
1.  05  515 
1.05  370 
1.  05  227 

9.  99  834 
9.  99  833 
9.  99  832 
9.  99  831 
9.  99  830 

60 

59 
58 
57 
56 

40   0 
56 
52 
48 
44 

20   20 
24 

28 
32 
36 

5 
6 

7 
8 
9 

8.  94  746 
8.  94  887 
8.  95  029 
8.95  170 
8.  95  310 

141 
142 
141 
140 
140 

8.  94  917 
8.  95  060 
8.  95  202 
8.  95  344 
8.  95  486 

143 
142 
142 
142 
141 

1.05  083 
1.04  940 
1.04  798 
1.  04  656 
1.04  514 

9.  99  829 
9.99828 
9.  99  827 
9.99  825 
9.  99  824 

55 
54 
53 

52 
51 

39  40 
36 
32 

28 
24 

20   40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

8.95  450 
8.  95  589 
8.  95  728 
8.  95  867 
8.%  005 

139 
139 
139 
138 
138 

8.  95  627 
8.  95  767 
8.  95  908 
8.%  047 
8.  96  187 

140 
141 
139 
140 
138 

1.  04  373 
1.04233 
1.  04  092 
1.03  953 
1.  03  813 

9.  99  823 
9.  99  822 
9.  99  821 
9.  99  820 
9.  99  819 

50 

49 
48 
47 
46 

39  20 
16 
12 

8 
4 

21   0 
4 
8 
12 

16 

15 
16 
17 
18 
19 

8.  96  143 
8.96  280 
8.  96  417 
8.96  553 
8.%  689 

137 
137 
136 
136 
136 

8.  96  325 
8.96  464 
8.96  602 
8.  96  739 
8.  %  877 

139 
138 
137 
138 
136 

1.  03  675 
1.03  536 
1.  03  398 
1.  03  261 
1.  03  123 

9.99  817 
9.  99  816 
9.  99  815 
9.  99  814 
9.99813 

45 
44 
43 
42 
41 

39   0 
56 
52 

48 
44 

21   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

8.%  825 
8.96  960 
8.97  095 
8.97  229 
8.97  363 

135 
135 
134 
134 
133 

8.  97  013 
8.  97  150 
8.  97  285 
8.  97  421 
8.97556 

137 
135 
136 
135 
135 

1.  02  987 
1.02  850 
1.02  715 
1.02  579 
1.  02  444 

9.  99  812 
9.  99  810 
9.99  809 
9.  99  808 
9.99807 

40 

39 
38 
37 
36 

38  40 
36 
32 

28 
24 

21   40 
44 
48 
52 
56 

25 

26 
27 

28 
29 

8.  97  496 
8.97  629 
8.  97  762 
8.97  894 
8.98026 

133 
133 
132 
132 
131 

8.  97  691 
8.  97  825 
8.97  959 
8.98  092 
8.  98  225 

134 
134 
133 
133 
133 

1.02  309 
1.02  175 
1.02  041 
1.  01  908 
1.01  775 

9.99  806 
9.  99  804 
9.99  803 
9.  99  802 
9.  99  801 

35 
34 
33 
32 
31 

38  20 
16 
12 
8 
4 

22   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

8.98  157 
8.98  288 
8.  98  419 
8.  98  549 
8.  98  679 

131 
131 
130 
130 
129 

8.98  358 
8.  98  490 
8.98  622 
8.  98  753 
8.98  884 

132 
132 
131 
131 
131 

1.01  642 
1.01  510 
1.01  378 
1.01  247 
1.01  116 

9.  99  800 
9.  99  798 
9.  99  797 
9.99  7% 
9.99  795 

30 

29 
28 
27 
26 

38   0 
56 
52 

48 
44 

22   20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

8.98  808 
8.  98  937 
8.99  066 
8.99  194 
8.  99  322 

129 
129 
128 
128 
128 

8.99015 
8.  99  145 
8.  99  275 
8.99  405 
8.  99  534 

130 
130 
130 
129 

128 

1.00  985 
1.00  855 
1.00  72$ 

L  00  466 

9.  99  793 
9.  99  792 
9.  99  791 
9.99  790 
9.  99  788 

25 

24 
23 
22 
21 

37  40 
36 
32 
28 
24 

22   40 
44 
48 
52 
56 

40 

41 
42 
43 

44 

8.99  450 
8.  99  577 
8.  99  704 
8.99  830 
8.99  956 

127 
127 
126 
126 
126 

8.99  662 
8.99  791 
8.  99  919 
9.00  046 
9.  00  174 

129 
128 
127 
128 
127 

1.00  338 
1.00  209 
1.00  081 
0.  99  954 
0.  99  826 

9.  99  787 
9.  99  786 
9.99  785 
9.  99  783 
9.  99  782 

20 

19 
18 
17 
16 

37  20 
16 
12 

8 
4 

23   0 
4 

8 
12 
16 

45 
46 
47 

48 
49 

9.  00  082 
9.00  207 
9.  00  332 
9.00  456 
9.00  581 

125 
125 
124 
125 
123 

9.  00  301 
9.  00  427 
9.  00  553 
9.  00  679 
9.00  805 

126 

126 
126 
126 
125 

0.  99  699 
0.  99  573 
0.  99  447 
0.  99  321 
0.  99  195 

9.  99  781 
9.  99  780 
9.  99  778 
9.  99  777 
9.  99  776 

15 
14 
13 
12 
11 

37   0 
56 
52 

48 
44 

23   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.00  704 
9.00  828 
9.  00  951 
9.  01  074 
9.01  196 

124 
123 
123 
122 
122 

9.  00  930 
9.  01  055 
9.01  179 
9.  01  303 
9.01427 

125 
124 
124 
124 
123 

0.  99  070 
0.  98  945 
0.  98  821 
0.  98  697 
0.98573 

9.  99  775 
9.  99  773 
9.  99  772 
9.99  771 
9.  99  769 

10 

9 

8 
7 
6 

36  40 
36 
32 

28 
24 

23   40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  01  318 
9.01  440 
9.01  561 
9.01  682 
9.01  803 

122 
121 
121 
121 
120 

9.01  550 
9.01  673 
9.01  796 
9.  01  918 
9.  02.  040 

123 
123 
122 
122 
122 

0.  98  450 
0.  98  327 
0.98204 
0.  98  082 
0.  97  960 

9.  99  768 
9.99  767 
9.99  765 
9.  99  764 
9.99  763 

5 
4 
3 
2 
1 

36  20 
16 
12 
8 
4 

24   0 

60 

9.01  923 

9.02  162 

0.97  838 

9.99  761 

0 

36   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

/ 

m.  s. 

84 


154  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

&  6° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

24   0 
4 
,   8 
12 
16 

0 

1 
2 
3 

4 

9.  01  923 
9.02043 
9.«02  163 
9.  02  283 
9.  02  402  . 

120 
120 
120 
119 
118 

9.  02  162 
9.02  283 
9.  02  404 
9.  02  525 
9.  02  645 

121 
121 
121 
120 
121 

0.97  838 
0.97  717 
0.  97  596 
0.  97  475 
0.97  355 

9.  99  761 
9.  99  760 
9.  99  759 
9.  99  757 
9.  99  756 

60 

59 

58 
57 
56 

36   0 
56 
52 

48 
44 

24  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  02  520 
9.  02  639 
9.02  757 
9.  02  874 
9.  02  992 

119 
118 
117 
118 
117 

9.02  766 
9.02  885 
9.03  005 
9.  03  124 
9.  03  242 

119 
120 
119 
118 
119 

0.97  234 
0.  97  115 
0.  96  995 
0.96  876 
0.  96  758 

9.  99  755 
9.  99  753 
9.  99  752 
9.  99  751 
9.  99  749 

55 
54 
53 
52 
51 

35  40 
36 
32 
28 
24 

24  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9,03  109 
9.  03  226 
9.  03  342 
9.  03  458 
9.  03  574 

117 
116 
116 
116 
116 

9.  03  361 
9.  03  479 
9.  03  597 
9.  03  714 
9.03  832 

118 
118 
117 
118 
116 

0.  96  639 
0.  96  521 
0.  96  403 
0.%  286 
0.96  168 

9.  99  748 
9.  99  747 
9.99  745 
9.99  744 
9.  99  742 

50 

49 
48 
47 
46 

35  20 
16 
12 

8 
4 

25   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.03  690 
9.  03  805 
9.03  920 
9.04  034 
9.  04  149 

115 
115 
114 
115 
113 

9.  03  948 
9.  04  065 
9.  04  181 
9.  04  297 
9.04  413 

117 
116 
116 
116 
115 

0.  96  052 
0.95  935 
0.  95  819 
0.  95  703 
0.  95  587 

9.  99  741 
9.  99  740 
9.99  738 
9.  99  737 
9.  99  736 

45 
44 
43 
42 
41 

35   0 
56 
52 
48 
44 

25  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  04  262 
9.  04  376 
9.04  490 
9.04  60? 
9.04  715 

114 
114 
113 
112 
113 

9.  04  528 
9.04  643 
9.04  758 
9.  04  873 
9.  04  987 

115 
115 
115 
114 
114 

0.  95  472 
0.  95  357 
0.  95  242 
0.  95  127 
0.  95  013 

9.  99  734 
9.  99  733 
9.  99  731 
9.  99  730 
9.99  728 

40 

39 
38 
37 
36 

34  40 
36 
32 
28 
24 

25  40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.  04  828 
9.  04  940 
9.  05  052 
9.  05  164 
9.  05  275 

112 
112 
112 
111 
111 

9.  05  101 
9.  05  214 
9.05  328 
9.  05  441 
9.05  553 

113 
114 
113 
112 
113 

0.  94  899 
0.94  786 
0.  94  672 
0.  94  559 
0.94  447 

9.  99  727 
9.  99  726 
9.99  724 
9.  99  723 
9.  99  721 

35 
34 
33 
32 
31 

34  20 
16 
12 
8 
4 

26   0 
4 
8 
12 
16 

80 

31 
32 
33 
34 

9.05  386 
9.  05  497 
9.  05  607 
9.  05  717 

9.  05  827 

111 
110 
110 
110 
110 

9.  05  666 
9.  05  778 
9.  05  890 
9.06  002 
9.06  113 

112 
112 
112 
111 
111 

0.94  334 
0.  94  222 
0.  94  110 
0.  93  998 
0.93  887 

9.  99  720 
9.99  718 
9.  99  717 
9.  99  716 
9.  99  714 

80 

29 
28 
27 
26 

34   0 
56 
52 
48 
44 

26  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  05  937 
9.06  046 
9.06  155 
9.06  264 
9.06  372 

109 
109 
109 
108 
109 

9.  06  224 
9.  06  335 
9.  06  445 
9.06  556 
9.  06  666 

111 
110 
111 
110 
109 

0.  93  776 
0.  93  665 
0.  93  555 
0.  93  444 
0.  93  334 

9.  99  713 
9.  99  711 
9.99  710 
9.  99  708 
9.  99  707 

25 
24 
23 
22 
21 

33  40 
36 
32 
28 
24 

26  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.06  481 
9.  06  589 
9.  06  696 
9.06  804 
9.06  911 

108 
107 
108 
107 
107 

9.  06  775 
9.06  885 
9.06  994 
9.  07  103 
9.  07  211 

110 
109 
109 
108 
109 

0.93  22§ 
0.  93  115 
0.  93  006 
0.  92  897 
0.  92  789 

9.  99  705 
9.99  704 
9.  99  702 
9.  99  701 
9.  99  699 

20 

19 
18 
17 
16 

33  20 
16 
12 
8 
4 

27   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.07  018 
9.07  124 
9.  07  231 
9.  07  337 
9.  07  442 

106 
107 
106 
105 
106 

9.07  320 
9.  07  428 
9.07  536 
9.  07  643 
9.07  751 

108 
108 
107 
108 
107 

0.92  680 
0.  92  572 
0.9*2  464 
0.  92  357 
0.  92  249 

9.  99  698 
9.99  696 
9.  99  695 
9.  99  693 
9.  99  692 

15 
14 
13 
12 
11 

33   0 
56 
52 
48 
44 

27  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  07  548 
9.  07  653 
9.07  758 
9.  07  863 
9.  07  968 

105 
105 
105 
105 
104 

9.  07  858 
9.07  964 
9.  08  071 
9.  08  177 
9.  08  283 

106 
107 
106 
106 
106 

0.92  142 
0.  92  036 
0.91  929 
0.91  823 
0.  91  717 

9.  99  690 
9.  99  689 
9.  99  687 
9.  99  686 
9.  99  684 

10 

9 

8 
7 
6 

32  40 
.36 
32 

28 
24 

27  40 
44 
48 
52 
56 

55 

56 
57 
58 
59 

9.  08  072 
9.08  176 
9.  08  280 
9.  08  383 
9.  08  486 

104 
104 
103 
103 
103 

9.08  389 
9.08  495 
9.08  600 
9.  08  705 
9.  08  810 

106 
105 
105 
105 
104 

0.91  611 
0.91  505 
0.  91  400 
0.  91  295 
0.  91  190 

9.  99  683 
9.  99  681 
9.  99  680 
9.  99  678 
9.  99  677 

5 
4 
3 
2 
1 

32  20 
16 
12 
8 
4 

28   0 

60 

9.08  589 

9.  08  914 

0.  91  086 

9.  99  675 

0 

32   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

' 

m.  s. 

83° 


5h 


GEOGEAPHIC  TABLES  AND  FORMULAS. 


155 


TABLE  22. — five-place  logarithms  of  circular  functions,  etc. — Continued. 
Ah  ijro 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

28   0 
4 
8 
12 
16 

?> 

2 
3 
4 

9.  08  589 
9.08  692 
9.08  795 
9.  08  897 
9.08  999 

103 

103 
102 
102 
102 

9.  08  914 
9.  09  019 
9.  09  123 
9.  09  227 
9.09  330 

105 
104 
104 
103 
104 

0.  91  086 
0.  90  981 
0.  90  877 
0.  90  773 
0.  90  670 

9.99  675 
9.  99  674 
9.99  672 
9.99  670 
9.  99  669 

60 

59 
58 
57 
56 

32   0 

56 
52 
48 
44 

28  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  09  101 
9.09  202 
9.09  304 
9.09  405 
9.09506 

101 
102 
101 
101 
100 

9.  09  434 
9.09  537 
9.09  640 
9.09  742 
9.09  845 

103 

103 
102 
103 
102 

0.90  566 
0.90  463 
0.90  360 
0.  90  258 
0.90  155 

9.  99  667 
9.99  666 
9.  99  664 
9.99  663 
9.  99  661 

55 
54 
53 
52 
51 

31  40 
36 
32 

28 
24 

28  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.09  606 
9.09  707 
9.09807 
9.09  907 
9.  10  006 

101 
100 
100 
99 
100 

9.  09  947 
9.  10  049 
9.  10  150 
9.  10  252 
9.  10  353. 

102 
101 
102 
101 
101 

0.90053 
0.  89  951 
0.  89  a50 
0.  89  748 
0.  89  647 

9.99  659 
9.99  658 
9.  99  656 
9.  99  655 
9".  99  653 

50 

59 
48 
47 
46 

31  20 
16 
12 
8 
4 

29   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  10  106 
9.  10  205 
9.10  304 
9.10  402 
9.  10  501 

99 

99 
98 
99 
98 

9.  10  454 
9.10  555 
9.10  656 
9.  10  756 
9.10  856 

101 
101 
100 
100 
100 

0.  89  546 
0.  89  445 
0.  89  344 
0.89  244 
0.89  144 

9.  99  651 
9.99  650 
9.  99  648 
9.99  647 
9.99  645 

45 
44 
43 
42 
41 

31   0 
56 
52 
48 
44 

29  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  10  599 
9.  10  697 
9.  10  795 
9.  10  893 
9.10  990 

98 
98 
98 
97 
97 

9.  10  956 
9.11  056 
9.  11  155 
9.  11  254 
9.11  353 

100 
99 
99 
99 
99 

0.  89  044 
0.88  944 
0.88  845 
0.88  746 
0.88  647 

9.  99  643 
9.  99  642 
9-.  99  640 
9.  99  638 
9.  99  637 

40 

39 
38 
37 
36 

30  40 
36 
32 
28 
24 

29  40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.11  087 
9.  11  184 
9.11  281 
9.  11  377 
9.  11  474 

97 
97 
96 
97 
% 

9.  11  452 
9.11  551 
9.  11  649 
9.  11  747 
9.11  845 

99 
98 
98 
98 

98 

0.88  548 
0.88  449 
0.  88  351 
0.88  253 
0.88  155 

9.99  635 
9.99  633 
9.  99  632 
9.  99  630 
9.  99  629 

35 
34 
33 
32 
31 

30  20 
16 
12 
8 
4 

30   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.11  570 
9.11  666 
9.11  761 
9.  11  857 
9.11  952 

96 
95 
96 
95 
95 

9.11  943 
9.12  040 
9.  12  138 
9.  12  235 
9.  12  332 

97 
98 
97 
97 
96 

0.  88  057 
0.87  960 
0.87  862 
0.87  765 
0.87  668 

9.  99  627 
9.99  625 
9.99  624 
9.  99  622 
9.99  620 

30 

29 
28 
27 
26 

30   0 
56 
52 
48 
44 

30  20 
24 
28 
32 
36 

35 

36 
37 
38 
39 

9.  12  047 
9.  12  142 
9.  12  236 
9.  12  331 
9.  12  425 

95 
94 
95 
94 
94 

9.  12  428 
9.12  525 
9.  12  621 
9.  12  717 
9.  12  813 

97 
96 
96 
96 
96 

0.  87  572 
0.  87  475 
0.  87  379 
0.  87  283 
0.  87  187 

9.  99  618 
9.99  617 
9.  99  615 
9.  99  613 
9.99  612 

25 
24 
23 

22 
21 

29  40 
36 
32 

28 
24 

30  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  12  519 
9.  12  612 
9.  12  706 
9.  12  799 
9.  12  892 

93 
94 
93 
93 
93 

9.12  909 
9.13  004 
9.13  099 
9.  13  194 
9.  13  289 

95 
95 
95 
95 
95 

0.  87  091 
0.86  996 
0.  86  901 
0.86  806 
0.  86  711 

9.  99  610 
9.99  608 
9.  99  607 
9.99  605 
9.  99  603 

20 

19 
18 
17 
16 

29  20 
16 
12 
8 
4 

31   0 

4 
8 
12 
16 

45 
46 
47 
48 
49 

9.  12  985 
9.  13  078 
9.  13  171 
9.  13  263 
9.13  355 

93 
93 
92 
92 
92 

9.13  384 
9.13  478 
9.  13  573 
9.  13  667 
9.  13  761 

94 
95 
94 
94 
93 

0.  86  616 
0.86  522 
0.86  427 
0.  86  333 
0.  86  239 

9.99  601 
9.99  600 
9.  99  598 
9.  99  596 
9.99  595 

15 
14 
13 
12 
11 

29   0 
56 
52 
48 
44 

31  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  13  447 
9.  13  539 
9.  13  630 
9.  13  722 
9.  13  813 

92 
91 
92 
91 
91 

9.13  854 
9.  13  948 
9.14  041 
9.  14  134 
9.  14  227 

94 
93 
93 
93 
93 

0.86  146 
0.86  052 
0.85  959 
0.85  866 
0.85  773 

9.  99  593 
9.  99  591 
9.  99  589 
9.99  588 
9.99  586 

10 

9 

8 
7 
6 

28  40 
36 
32 
28 
24 

31  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.13  904 
9.13  994 
9.  14  085 
9.  14  175 
9.  14  266 

90 
91 
90 
91 
90 

9.  14  320 
9.  14  412 
9.14  504 
9.  14  697 
9.  14  688 

92 
92 
93 
91 
92 

0.85  680 
0.85  588 
0.85  4% 
0.85  403 
0.85  312 

9.99  584 
9.99  582 
9.99  581 
9.  99  579 
9.  99  677 

5 
4 
3 
2 
1 

28  20 
16 
12 
8 
4 

32   0 

60 

9.  14  356 

9.  14  780 

0.86  220 

9.99  575 

0 

28   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

i 

m.  s. 

156  GEOGRAPHIC    TABLES    AND    FOKMULA.8. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  8° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

32   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.14  356 
9.  14  445 
9.  14  535 
9.  14  624 
9.  14  714 

89 
90 
89 
90 
89 

9.  14  780 
9.  14  872 
9.  14  963 
9.  15  054 
9.  15  145 

92 
91 
91 
91 
91 

0.  85  220 
0.  85  128 
0.  85  037 
0.  84  946 
0.84  855 

9.  99  575 
9.  99  574 
9.  99  572 
9.  99  570 
9.  99  568 

60 

59 

58 
57 
56 

28   0 
56 
52 
48 
44 

32   20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  14  803 
9.  14  891 
9.  14  980 
9.  15  069 
9.  15  157 

88 
89 
89 
88 

88 

9.  15  236 
9.  15  327 
9.  15  417 
9.  15  508 
9.  15  598 

91 
90 
91 
90 
90 

0.84  764 
0.  84  673 
0.  84  583 
0.  84  492 
0.  84  402 

9.  99  566 
9.99  565 
9.  99  563 
9.  99  561 
9.  99  559 

55 
54 
53 
52 
51 

27  40 
36 
32 
28 
24 

32   40 
44 

48 
52 
56 

10 

11 

12 
13 
14 

9.  15  245 
9.  15  333 
9.  15  421 
9.  15  508 
9.  15  596 

88 
88 
87 
88 
87 

9.  15  688 
9.  15  777 
9.  15  867 
9.  15  956 
9.  16  046 

89 
90 
89 
90 
89 

0.  84  312 
0.  84  223 
0.  84  133 
0.  84  044 
0.  83  954 

9.  99  557 
9.99  556 
9.99  554 
9.  99  552 
9.  99  550 

50 

49 
48 
47 
46 

27  20 
16 
12 
8 
4 

33   0 
4 
8 
12 
16 

15 
16 
17 

18 
19 

9.15  683 
9.15  770 
9.  15  857 
9.  15  944 
9.  16  030 

87 
87 
87 
86 
86 

9.  16  135 
9.  16  224 
9.  16  312 
9.  16  401 
9.  16  489 

89 
88 
89 
88 
88 

0.83  865 
0.  83  776 
0.  83  688 
0.83  599 
0.  83  511 

9.  99  548 
9.  99  546 
9.  99  545 
9.99  543 
9.  99  541 

45 
44 
43 
42 
41 

27   0 
56 
52 
48 
44 

33   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.16  116 
9.  16  203 
9.  16  289 
9.  16  374 
9.  16  460 

87 
86 
85 
86 

85 

9.  16  577 
9.16  665 
9.  16  753 
9.  16  841 
9.  16  928 

88 
88 
88 
87 
88 

0.  83  423 
0.  83  335 
0.  83  247 
0.  83  159 
0.  83  072 

9.  99  539 
9.  99  537 
9.  99  535 
9.  99  533 
9.  99  532 

40 

39 
38 
37 
36 

26  40 
36 
32 
28 
24 

33   40 

44 
48 
52 
56 

25 
26 
27 
28 
29 

9.16  545 
9.  16  631 
9.  16  716 
9.  16  801 
9.16  886 

86 
85 

85 
85 
84 

9.  17  016 
9.  17  103 
9.  17  190 
9.  17  277 
9.  17  363 

87 
87 
87 
86 
87 

0.  82  984 
0.  82  897 
0.  82  810 
0.82  723 
0.82  637 

9.  99  530 
9.  99  528 
9.  99  526 
9.  99  524 
9.  99  522 

35 
34 
33 
32 
31 

26  20 
16 
12 
8 
4 

34   0 
4 

8 
12 
16 

30 

31 
32 
33 
34 

9.  16  970 
9.  17  055 
9.  17  139 
9.  17  223 
9.  17  307 

85 
84 
84 
84 
84 

9.  17  450 
9.  17  536 
9.  17  622 
9.  17  708 
9.  17  794 

86 
86 
86 
86 
86 

0.  82  550 
0.  82  464 
0.  82  378 
0.  82  292 
0.  82  206 

9.  99  520 
9.  99  518 
9.  99  517 
9.  99  515 
9.  99  513 

30 

29 

28 
27 
26 

26   0 
56 
62 
48 
44 

34   20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  17  391 
9.  17  474 
9.  17  558 
9.  17  641 
9.  17  724 

83 
84 
83 
83 
83 

9.17  88Q 
9.  17  965 
9.  18  051 
9.18  136 
9.  18  221 

85 
86 
85 
85 
85 

0.  82  120 
0.  82  035 
0.  81  949 
0.81  864 
0.81  779 

9.  99  511 
9.  99  509 
9.99  507 
9.  99  505 
9.  99  503 

25 
24 
23 
22 
21 

25  40 
36 
32 

28 
24 

34   40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  17  807 
9.  17  890 
9.  17  973 
9.  18  055 
9.  18  137 

83 
83 

82 
82 
83 

9.  18  306 
9.  18  391 
9.  18  475 
9.18  560 
9.  18  644 

85 
84 
85 
84 
84 

0.81  694 
0.  81  609 
0.  81  525 
0.  81  440 
0.  81  356 

9.  99  501 
9.  99  499 
9.  99  497 
9.  99  495 
9.  99  494 

20 

19 
18 
17 
16 

25  20 
16 
12 

8 
4 

35   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.  18  220 
9.  18  302 
9.  18  383 
9.  18  465 
9.  18  547 

82 
81 
82 
82 
81 

9.  18  728 
9.  18  812 
9.  18  896 
9.18  979 
9.  19  063 

84 
84 
83 
84 
83 

0.81  272 
0.81  188 
0.81  104 
0.  81  021 
0.  80  937 

9.  99  492 
9.99  490 
9.  99  488 
9.  99  486 
9.  99  484 

15 
14 
13 
12 
11 

25   0 
56 
52 

48 
44 

35   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  18  628 
9.  18  709 
9.  18  790 
9.  18  871 
9.  18  95? 

81 
81 
81 
81 
81 

9.  19  146 
9.  19  229 
9.  19  312 
9.  19  395 
9.  19  478 

83 
83 
83 
83 
83 

0.  80  854 
0.  80  771 
0.80  688 
0.  80  605 
0.  80  522 

9.  99  482 
9.  99  480 
9.  99  478 
9.  99  476 
9.  99  474 

10 

9 

8 
7 
6 

24  40 
36 
32 
28 
24 

35   40 

44 
48 
52 
56 

55 

56 
57 
58 
59 

9.  19  033 
9.19  113 
9.19  193 
9.  19  273 
9.  19  353 

80 
80 
80 
80 
80 

9.  19  561 
9.  19  643 
9.  19  725 
9.  19  807 
9.  19  889 

82 
82 
82 
82 

82  ' 

0.  80  439 
0.  80  357 
0.80  275 
0.  80  193 
0.  80  111 

9.  99  472 
9.99  470 
9.99  468 
9.  99  466 
9.  99  464 

5 
4 
3 
2 
1 

24  20 
16 
12 

8 
4 

36   0 

60 

9.  19  433 

9.  19  971 

0.  80  029 

9.  99  462 

0 

24   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

' 

m.  s. 

81C 


5h 


GEOGRAPHIC    TABLES    AND   FORMULAS. 


157 


TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  9° 


m.   s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

36   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  19  433 
9.  19  513 
9.  19  592 
9.  19  672 
9.  19  751 

80 
79 
80 
79 
79 

9.  19  971 
9.  20  053 
9.20  134 
9.  20  216 
9.  20  297 

82 
81 
82 
81 
81 

0.  80  029 
0.  79  947 
0.  79  866 
0.  79  784 
0.  79  703 

9.  99  462 
9.  99  460 
9.  99  458 
9.99  156 
9.99  454 

60 

59 
58 
57 
56 

24   0 
56 
52 
48 
44 

36   20 
24 

28 
32 
36 

5 
6 
7 
8 
9 

9.19  830 
9.19  909 
9.  19  988 
9.  20  067 
9.20  145 

79 
79 
79 

78 
78 

9.  20  378 
9.  20  459 
9.20  540 
9.  20  621 
9.  20  701 

81 
81 
81 
80 
81 

0.  79  622 
0.  79  541 
0.  79  460 
0.  79  379 
0.  79  299 

9.99  452 
9.  99  450 
9.  99  448 
9.99  446 
9.99  444 

55 
54 
53 

52 
51 

23  40 
36 
32 
28 
24 

36   40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  20  223 
9.20  302 
9.20  380 
9.20  458 
9.20  535 

79 
78 
78 
77 
78 

9.20  782 
9.  20  862 
9.  20  942 
9.21  022 
9.21  102 

80 
80 
80 
80 
80 

0.  79  218 
0.  79  138 
0.  79  058 
0.  78  978 
0.  78  898 

9.  99  442 
9.  99  440 
9.  99  438 
9.  99  436 
9.  99  434 

50 

49 
48 
47 
46 

23  20 
16 
12 
8 
4 

37   0 
4 

8 
12 
16 

15 
16 
17 
18 
19 

9.  20  613 
9.  20  691 
9.  20  768 
9.20  845 
9.20  922 

78 
77 
77 
77 
77 

9.21  182 
9.21  261 
9.21  341 
9.21  420 
9.21  499 

79 
80 
79 
79 
79 

0.  78  818 
0.  78  739 
0.  78  659 
0.78  580 
0.  78  501 

9.  99  432 
9.  99  429 
9.  99  427 
9.99  425 
9.99423 

45 
44 
43 
42 
41 

23   0 

56 
52 
48 
44 

37   20 
24 
28 
32 
36 

20 

21 

22 
23 

•24 

9.20999 
9.  21  076 
9.21  153 
9.21  229 
9.21  306 

77 
77 
76 
77 
76 

9.21  578 
9.21  657 
9.21  736 
9.21  814 
9.  21  893 

79 
79 

78 
79 
78 

0.  78  422 
0.  78  343 
0.  78  264 
0.  78  186 
0.78  107 

9.  99  421 
9.99  419 
9.99417 
9.  99  415 
9.  99  413 

40 

39 
38 
37 
36 

22  40 
36 
32 
28 
24 

37   40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

9.21  382 
9.21  458 
9.21  534 
9.  21  610 
9.21  685 

76 
76 
76 
75 
76 

9.  21  971 
9.22  049 
9.22  127 
9.22  205 
9.22  283 

78 
78 
78 
78 
78 

0.78029 
0.  77  951 
0.  77  873 
0.  77  795 
0.  77  717 

9.99  411 
9.99  409 
9.  99  407 
9.  99  404 
9.99  402 

35 
34 
33 
32 
31 

22  20 
16 
12 
8 
4 

38   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.21  761 
9.21  836 
9.21  912 
9.21  987 
9.22  062 

75 
76 
75 

75 
75 

9.22  361 
9.22  438 
9.22  516 
9.22  593 
9.22  670 

77 
78 

77 
77 
77 

0.  77  639 
0.  77  562 
0.  77  484 
0.  77  407 
0.  77  330 

9.99  400 
9.99  398 
9.  99  396 
9.99  394 
9.99  392 

30 

29 

28 

26 

22   0 
56 
52 

% 

38   20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  22  137 
9.22  211 
9.22  286 
9.22  361 
9.22  435 

74 
75 
75 
74 
74 

9.22  747 
9.22  824 
9.  22  901 
9.22  977 
9.23054 

77 
77 
76 
77 
76 

0.  77  253 
0.77  176 
0.  77  099 
0.  77  023 
0.  76  946 

9.99  390 
9.99  388 
9.99  385 
9.  99  383 
9.99  381 

25 
24 
23 
22 
21 

21  40 
36 
32 

28 
24 

38   40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.22  509 
9.22  583 
9.22  657 
9.22  731 
9.22  805 

74 
74 
74 
74 

73 

9.23  130 
9.23  206 
9.23  283 
9.  23  359 
9.  23  435 

76 
77 
76 
76 

75 

0.  76  870 
0.  76  794 
0.  76  717 
0.  76  641 
0.  76  565 

9.99  379 
9.  99  377 
9.99  375 
9.  99  372 
9.  99  370 

20 

19 

18 
17 
16 

21  20 

16 
12 
8 
4 

39   0 
4 
8 
12 
16 

45 
46 

47 
48 
49 

9.  22  878 
9.22  952 
9.23  025 
9.  23  098 
9.23  171 

74 
73 
73 
73 
73 

9.23  510 
9.  23  586 
9.  23  661 
9.23  737 
9.  23  812 

76 
75 
76 
75 
75 

0.  76  490 
0.  76  414 
0.  76  339 
0.  76  263 

0.  76  188 

9.99  368 
9.  99  366 
9.  99  364 
9.  99  362 
9.  99  359 

15 
14 
13 
12 
11 

21   0 
56 
52 
48 
44 

39   20 
24 
28 
32 
86 

50 

51 
52 
53 
54 

9.23  244 
9.23  317 
9.23  390 
9.23  462 
9.23  535 

73 
73 
72 
73 

72 

9.23  887 
9.23  962 
9.24  037 
9.  24  112 
9.24  186 

75 
75 
75 
74 

0.  76  113 
0.  76  038 
0.  75  963 
0.  75  888 
0.  75  814 

9.99  357 
9.99  355 
9.  99  353 
9.99  351 
9.99  348 

10 

9 

8 
7 
6 

20  40 
36 
32 
28 
24 

39   40 
44 
48 
52 
56 

K 

56 
57 

58 
59 

9.23  607 
9.  23  679 
9.23  752 
9.23  823 
9.23  895 

72 
73 
71 
72 

72 

9.24  261 
9.24  335 
9.24  410 
9.  24  484 
9.24  558 

74 
75 
74 

74 
74 

0.  75  739 
0.75  665 
0.  75  590 
0.  75  516 
0.  75  442 

9.  99  346 
9.99  344 
9.  99  342 
9.  99  340 
9.  99  337 

5 

4 

2 
1 

20  20 
16 
12 
8 
4 

40   0 

60 

9.23  967 

9.24  632 

0.  75  368 

9.99  335 

0 

20   0 

L.COS. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

' 

m.   s. 

80° 


158          GEOGKAPHIC  TABLES  AND  FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  10° 


m.  s. 

• 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

40   0 
4 
8 
12 
16 

0 

1 

2 

4 

9.23  967 
9.24  039 
9.  24  110 
9.  24  181 
9.  24  253 

72 
71 
71 

72 

9.  24  632 
9.  24  706 
9.  24  779 
9.  24  853 
9.  24  926 

74 
73 
74 
73 
74. 

0.75  368 
0.  75  294 
0.  75  221 
0.  75  147 
0.  75  074 

9.99  335 
9.  99  333 
9.  99  331 
9.  99  328 
9.  99  326 

2 
2 
3 
2 

60 

59 

58 
57 
56 

20   0 
56 
52 
48 
44 

40  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  24  324 
9.  24  395 
9.  24  466 
9.  24  536 
9.  24  607 

71 
71 
70 
71 

9.25  000 
9.  25  073 
7.  25  146 
9.  25  219 
9.  25  292 

73 
73 
73 
73 
70 

0.  75  000 
0.  74  927 
0.74  854 
0.  74  781 
0.  74  708 

9.  99  324 
9.  99  322 
9.  99  319 
9.  99  317 
9.  99  315 

2 
3 
2 

2 

55 
54 
53 
52 
51 

19  40 
36 
32 
28 
24 

40  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  24  677 
9.  24  748 
9.  24  818 
9.24  888 
9.  24  958 

71 
70 
70 
70 

9.  25  365 
9.  25  437 
9.  25  510 
9.  25  582 
9.  25  655 

72 
73 
72 
73 
79 

0.  74  635 
0.  74  563 
0.  74  490 
0.  74  418 
0.  74  345 

9.  99  313 
9.99  310 
9.  99  308 
9.  99  306 
9.99  304 

3 
2 
2 
2 

50 

49 
48 
47 
46 

19  20 
16 
12 

8 
4 

41   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  25  028 
9.  25  098 
9.25  168 
9.  25  237 
9.25  307 

70 

70 
69 
70 

9.25  727 
9.25  799 
9.  25  871 
9.  25  943 
9.26  015 

72 
72 
72 
72 

0.  74  273 
0.  74  201 
0.  74  129 
0.  74  057 
0.  73  985 

9.99  301 
9.  99  299 
9.  99  297 
9.  99  294 
9.99  292 

2 
2 
3 
2 

45 
44 
43 
42 
41 

19   0 
56 
52 
48 
44 

41  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.25376 
9.  25  445 
9.  25  514 
9.25  583 
9.  25  652 

69 
69 
69 
69 

9.  26  086 
9.  26  158 
9.  26  229 
9.  26  301 
9.  26  372 

72 
71 
72 
71 

0.  73  914 
0.  73  842 
0.  73  771 
0.  73  699 
0.  73  628 

9.  99  290 
9.  99  288 
9.  99  285 
9.99  283 
9.  99  281 

2 
3 
2 

2 

40 

39 
38 
37 
36 

18  40 
36 
32 
28 
24 

41.  40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

9.  25  721 
9.  25  790 
9.25  858 
9.  25  927 
9.  25  995 

69 

68 
69 
68 

GO 

9.  26  443 
9.26  514 
9.  26  585 
9.  26  655 
9.  26  726 

71 
71 

70 
71 

0.  73  557 
0.  73  486 
0.  73  415 
0.  73  345 
0.  73  274 

9.99  278 
9.  99  276 
9.  99  274 
9.  99  271 
9.  99  269 

2 
2 
3 
2 

35 
34 
33 
32 
31 

18  20 
16 
12 
8 
4 

42   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.26  063 
9.  26  131 
9.  26  199 
9.  26  267 
9.  26  335 

68 
68 
68 
68 
68 

9.26  797 
9.26  867 
9.26  937 
9.27  008 
9.  27  078 

70 
70 
71 
70 

0.  73  203 
0.  73  133 
0.  73  063 
0.72  992 
0.  72  922 

9.  99  267 
9.99  264 
9.  99  262 
9.  99  260 
9.99  257 

3 
2 
2 
3 

30 

29 
28 
27 
26 

18   0 
56 
52 
48 
44 

42  20 
24 
28 
32 
36 

35 
36 
37 

38 
39 

9.  26  403 
9.  26  470 
9.26  538 
9.26  605 
9.26  672 

67 
68 
67 
67 
fi7 

9.27  148 
9.  27  218 
9.27  288 
9.  27  357 
9.27  427 

70 
70 
69 
70 

0.  72  852 
0.  72  782 
0.  72  712 
0.  72  643 
0.  72  573 

9.  99  255 
9.  99  2o2 
9.99  250 
9.  99  248 
9.99  245 

3 
2 
2 
3 

25 
24 
23 
22 
21 

17  40 
36 
32 
28 
24 

42  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  26  739 
9.26  806 
9.  26  873 
9.  26  940 
9.27  007 

67 
67 
67 
67 

9.  27  496 
9.27  566 
9.  27  635 
9.27  704 
9.  27  773 

70 
69 
69 
69 

0.72  504 
0.  72  434 
0.  72  365 
0.  72  296 
0.  72  227 

9.  99  243 
9.  99  241 
9.  99  238 
9.  99  236 
9.99  233 

2 
3 
2 
3 

20 

19 
18 
17 
16 

17  20 
16 
12 
8 
4 

43   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.  27  073 
9.  27  140 
9.27  206 
9.  27  273 
9.27  339 

67 
66 
67 
66 

9.27  842 
9.27  911 
9.  27  980 
9.  28  049 
9.  28  117 

69 
69 
69 
68 

0.72  158 
0.  72  089 
0.  72  020 
0.  71  951 
0.  71  883 

9.  99  231 
9.  99  229 
9.  99  226 
9.  99  224 
9.99  221 

2 
3 
2 
3 

15 
14 
13 
12 
11 

17   0 

56 
52 
48 
44 

43  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.27  405 
9.  27  471 
9.27  537 
9.  27  602 
9.27  668 

66 
66 
65 
66 

9.28  186 
9.28  254 
9.28  323 
9.28  391 
9.  28  459 

68 
69 
68 
68 

0.71  814 
0.71  746 
0.  71  677 
0.71  609 
0.  71  541 

9.99  219 
9.99  217 
9.  99  214 
9.  99  212 
9.  99  209 

2 
3 
2 
3 

10 

9 

8 

7 
6 

16  40 
36 
32 

28 
24 

43  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.27  734 
9.  27  799 
9.  27  864 
9.  27  930 
9.  27  995 

65 
65 
66 
65 

9.  28  527 
9.  28  595 
9.  28  662 
9.  28  730 
9,  28  798 

68 
67 
68 
68 

0.  71  473 
0.71  405 
0.71  338 
0.  71  270 
0.71  202 

9.  99  207 
9.99  204 
9.  99  202 
9.  99  200 
9.  99  197 

3 

2 
2 
3 

5 
4 
3 
2 
1 

16  20 
16 
12 
8 
4 

44   0 

60 

9.28  060 

9.28  865 

0.71  135 

9.99  195 

0 

16   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

79° 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


159 


TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  11° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

44   0 
4 
8 
12 

16 

0 
1 
2 
3 
4 

9.28  060 
9.28  125 
9.28  190 
9.28254 
9.  28  319 

.  65 
65 
64 
65 

9.28  865 
9.28  933 
9.29  000 
9.29  067 
9.29  134 

68 
67 
67 
67 

0.  71  135 
0.71  067 
0.71  000 
0.70  933 
0.  70  866 

9.99  196 
9.99  192 
9.  99  190 
9.99  187 
9.  99  185 

3 
2 
3 
2 

60 

59 

58 
57 
56 

16   0. 

56 
52 
48 
44 

44  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.28  384 
9.28  448 
9.  28  512 
9.28  577 
9.28  641 

64 
64 
65 
64 

9.  29  201 
9.29  268 
9.29  335 
9.29402 
9.29  468 

67 
67 
67 
66 

0.  70  799 
0.  70  732 
0.  70  665 
0.  70  598 
0.  70  532 

9.99  182 
9.99  180 
9.  99  177 
9.  99  175 
9.  99  172 

2 
3 
2 

3 

55 
54 
53 

52 
51 

15  40 
36 
32 
28 
24 

44  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.28  705 
9.  28  769 
9.28  833 
9.28  896 
9.28  960 

64 
64 
63 
64 

9.29  535 
9.  29  601 
9.29  668 
9.  29  734 
9.29  800 

66 
67 
66 
66 

0.  70  465 
0.  70  399 
0.  70  332 
0.  70  266 
0.  70  200 

9.  99  170 
9.99  167 
9.99  165 
9.  99  162 
9.99  160 

3 

2 
3 
2 

50 

49 
48 
47 
46 

15  20 
16 
12 
8 
4 

45   0 
4 

8 
12 
16 

15 
16 
17 
18 
19 

9.29  024 
9.29087 
9.  29  150 
9.29  214 
9.  29  277 

63 

63 
64 
63 

9.  29  866 
9.29  932 
9.  29  998 
9.30  064 
9.  30  130 

66 
66 
66 
66 
fifi 

0.  70  134 
0.70068 
0.70  002 
0.  69  936 
0.  69  870 

9.  99  157 
9.  99  155 
9.  99  152 
9.99  150 
9.  99  147 

2 
3 
2 
3 

45 
44 
43 
42 
41 

15   0 

56 
52 
48 
44 

45  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.29  340 
9.  29  403 
9.29  466 
9.29  529 
9.29591 

63 
63 
63 
62 

9.30  195 
9.  30  261 
9.  30  326 
9.30  391 
9.  30  457 

66 
65 
65 
66 
fiS 

0.69  805 
0.  69  739 
0.  69  674 
0.69  609 
0.  69  543 

9.99  145 
9.  99  142 
9.  99  140 
9.  99  137 
9.  99  135 

3 
2 
3 
2 

40 

39 
38 
37 
36 

14  40 
36 
32 
28 
24 

45  40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.29  654 
9.29  716 
9.29  779 
9.  29  841 
9.29  903 

62 
63 
62 
62 
fiS 

9.  30  522 
9.30587 
9.30  652 
9.  30  717 
9.30782 

65 
65 
65 
65 
fi4 

0.  69  478 
0.69413 
0.  69  348 
0.  69  283 
0.  69  218 

9.  99  132 
9.99  130 
9.  99  127 
9.99  124 
9.99  122 

2 
3 
3 
2 

35 
34 
33 
32 
31 

14  20 
16 
12 
8 
4 

46   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.29966 
9.30  028 
9.30  090 
9.30  151 
9.  30  213 

62 
62 
61 
62 

9.30  846 
9.  30  911 
9.  30  975 
9.  31  040 
9.31  104 

65 
64 
65 
64 

0.  69  154 
0.  69  089 
0.  69  025 
0.68  960 
0.68  896 

9.99  119 
9.  99  117 
9.  99  114 
9.  99  112 
9.99  109 

2 
3 
2 
3 

30 

29 
28 
27 
26 

14   0 
56 
52 
48 
44 

46  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  30  275 
9.30  336 
9.  30  398 
9.30459 
9.  30  621 

61 
62 
61 
62 

9.31  168 
9.31  233 
9.31  297 
9.  31  361 
9.  31  425 

65 
64 
64 
64 

0.  68  832 
0.  68  767 
0.68  703 
0.  68  639 
0.68  575 

9.  99  106 
9.  99  104 
9.  99  101 
9.  99  099 
9.99  096 

2 
3 
2 
3 

25 
24 
23 
22 
21 

13  40 
36 
32 
28 

24 

46  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.30  582 
9.30  643 
9.  30  704 
9.  30  765 
9.30826 

61 
61 
61 
61 

9.  31  489 
9.31  552 
9.31  616 
9.31  679 
9.31  743 

63 
64 
63 
64 

0.  68  511 
0.  68  448 
0.  68  384 
0.  68  321 
0.  68  257 

9.  99  093 
9.  99  091 
9.  99  088 
9.99  086 
9.99  083 

2 
3 
2 
3 

20 

19 

18 
17 
16 

13  20 
16 
12 
8 
4 

47   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.30  887 
9.  30  947 
9.  31  008 
9.31  068 
9.31  129 

60 
61 
60 
61 

9.31  806 
9.31  870 
9.31  933 
9.31  996 
9.32059 

64 
63 
63 
63 

0.  68  194 
0.68  130 
0.  68  067 
0.68  004 
0.  67  941 

9.  99  080 
9.  99  078 
9.  99  075 
9.  99  072 
9.  99  070 

2 
3 
3 
2 

15 
14 
13 
12 
11 

13   0 

56 
52 
48 
44 

47  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.31  189 
9.31  250 
9.31  310 
9.31  370 
9.  31  430 

61 
60 
60 
60 

9.32122 
9.  32  185 
9.  32  248 
9.  32  311 
9.  32  373 

•63 
63 
63 
62 

0.  67  878 
0.  67  815 
0.  67  752 
0.67  689 
0.  67  627 

9.99  067 
9.99  064 
9.99  062 
9.  99  059 
9.  99  056 

3 
2 
3 
3 

10 

9 

8 
7 
6 

12  40 
36 
32 

28 
24 

47  40 
44 
48 
52 
56 

55 

56 
67 
58 
59 

9.  31  490 
9.  31  549 
9.31  609 
9.31  669 
9.31  728 

59 
60 
60 
59 

9:32  436 
9.  32  498 
9.  32  561 
9.  32  623 
9.32685 

62 
63 
62 
62 

0.67  564 
0.  67  502 
0.67  439 
0.67  377 
0.  67  315 

9.99  054 
9.  99  051 
9.  99  048 
9.99  046 
9.  99  043 

3 
3 
2 
3 

5 
4 
3 
2 
1 

12  20 
16 
12 
8 
4 

48   0 

60 

9.  31  788 

9.  32  747 

0.  67  253 

9.99  040 

0 

12   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

78° 


5h 


160  GEOGRAPHIC    TABLES    AND   FOKMULAS. 

.TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  12° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

48   0 
4 
8 
12 
16 

0 

1 

3 
4 

9.31  788 
9.  31  847 
9.31  907 
9.  31  966 
9.  32  025 

59 
60 
59 
59 
59 

59 
59 
59 
58 
59 

59 

58 
58 
59 

58 

58 
58 
58 
58 
58 

58 
57 
58 
57 
58 

57 
57 
58 
57 
57 

57 
56 
57 
57 
57 

56 
57 
56 
56 
57 

56 
56 
56 
56 
56 

56 
55 
56 
55 
56 

9.32  747 
9.  32  810 
9.  32  872 
9.  32  933 
9.  32  995 

63 
62 
61 
62 
62 

62 
61 
62 
61 
62 

61 
61 
61 
61 
61 

61 
61 
61 
60 
61 

60 
61 
60 
60 
61 

60 
60 
60 
60 
60 

59 
60 
60 
59 
60 

59 
59 
59 
60 
59 

59 
59 
59 

58 
59 

59 
58 
59 
58 
59 

58 
58 
58 
58 
58 

58 
58 
58 
58 
57 

0.  67  253 
0.67  190 
0.  67  128 
0.  67  067 
0.67  005 

9.  99  040 
9.  99  038 
9.  99  035 
9.  99  032 
9.  99  030 

2 
3 
3 
2 

3 

3 
2 
3 
3 
3 

2 
3 
3 
3 

2 

3 
3 
3 
2 
3 

3 
3 
2 
3 
3 

60 

59 
58 
57 
56 

12   0 
56 
52 

48 
44 

48  20 
24 
28 
32 
36 

5 

6 
7 
8 
9 

9.  32  084 
9.  32  143 
9.  32  202 
9.  32  261 
9.  32  319 

9.  33  057 
9.33  119 
9.  33  180 
9.  33  242 
9.  33  303 

0.  66  943 

0.  66  881 
0.  66  820 
0.66  758 
0.  66  697 

9.  99  027 
9.  99  024 
9.  99  022 
9.  99  019 
9.  99  016 

55 
54 
53 
52 
51 

11  40 
36 
32 
28 
24 

48  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  32  378 
9.  32  437 
9.  32  495 
9.  32  553 
9.  32  612 

9.  33  365 
9.  33  426 
9.  33  487 
9.  33  548 
9.33  609 

0.  66  635 
0.  66  574 
0.  66  513 
0.  66  452 
0.66  391 

9.  99  013 
9.99  Oil 
9.  99  008 
9.99  005 
9.  99  002 

50 

49 

48 
47 
46 

11  20 
16 
12 

8 
4 

49   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  32  670 
9.  32  728 
9.  32  786 
9.  32  844 
9.  32  902 

9.  33  670 
9.33  731 
9.  33  792 
9.  33  853 
9.  33  913 

0.  66  330 
0.  66  269 
0.  66  208 
0.  66  147 
0.66  087 

9.99  000 
9.98997 
9.  98  994 
9.98  991 
9.  98  989 

45 
44 
43 
42 
41 

11   0 
56 
52 
48 
44 

49  20 
24 

28 
32 
36 

20 

21 
22 
23 
24 

9.  32  960 
9.  33  018 
9.  33  075 
9.  33  133 
9.  33  190 

9.  33  974 
9.  34  034 
9.  34  095 
9.  34  155 
9.  34  215 

0.  66  026 
0.  65  966 
0.  65  905 
0.65  845 
0.  65  785 

9.  98  986 
9.  98  983 
9.  98  980 
9.  98  978 
9.  98  975 

40 

39 
38 
37 
36 

10  40 
36 
32 

28 
24 

49  40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.  33  248 
9.  33  305 
9.  33  362 
9.  33  420 
9.  33  477 

9.34276 
9.  34  336 
9.  34  396 
9.  34  456 
9.34516 

0.  65  724 
0.  65  664 
0.  65  604 
0.  65  544 
0.  65  484 

9.  98  972 
9.  98  969 
9.  98  967 
9.98  964 
9.  98  961 

3 
2 
3 
3 
3 

3 
2 
3 
3 
3 

3 
3 
2 
3 

3 
3 
3 
2 
3 

35 
34 
33 
32 
31 

10  20 
16 
12 

8 
4 

50   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.33  534 
9.  33  591 
9.  33  647 
9.  33  704 
9.  33  761 

9.  34  576 
9.  34  635 
9.  34  695 
9.  34  755 
9.  34  814 

0.  65  424 
0.  65  365 
0.  65  305 
0.  65  245 
0.  65  186 

9.  98  958 
9.  98  955 
9.  98  953 
9.  98  950 
9.  98  947 

30 

29 
28 
27 
26 

10   0 
56 
52 
48 
44 

50  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  33  818 
9.  33  874 
9.33  931 
9.  33  987 
9.  34  043 

9.  34  874 
9.  34  933 
9.34  992 
9.35051 
9.  35  111 

0.  65  126 
0.  65  067 
0.  65  008 
0.  64  949 
0.  64  889 

9.98  944 
9.  98  941 
9.98  938 
9.  98  936 
9.  98  933 

25 
24 
23 
22 
21 

9  40 
36 
32 
28 
24 

50  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  34  100 
9.  34  156 
9.  34  212 
9.  34  268 
9.  34  324 

9.35  170 
9.  35  229 
9.35  288 
9.  35  347 
9.  35  405 

0.  64  830 
0.64  771 
0.  64  712 
0.  64  653 
0.  64  595 

9.  98  930 
9.  98  927 
9.  98  924 
9.  98  921 
9.  98  919 

20 

19 
18 
17 
16 

9  20 
16 
12 

8 
4 

51   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.  34  380 
9.  34  436 
9.  34  491 
9.  34  547 
9.  34  602 

9.35464 
9.  35  523 
9.35  581 
9.  35  640 
9.35  698 

0.  64  536 
0.64  477 
0.  64  419 
0.64  360 
0.64  302 

9.  98  916 
9.  98  913 
9.  98  910 
9.  98  907 
9.  98  904 

3 
3 
3 
3 
3 

15 
14 
13 
12 
11 

9   0 

56 
52 
48 
44 

51  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.34  658 
9.  34  713 
9.  34  769 
9.  34  824 
9.  34  879 

55 
56 
55 
55 
55 

9.  35  757 
9.  35  815 
9.  35  873 
9.  35  931 
9.  35  989 

0.  64  243 
0.  64  185 
0.64  127 
0.  64  069 
0.  64  Oil 

9.  98  901 
9.  98  898 
9.  98  896 
9.  98  893 
9.  98  890 

3 
2 
3 
3 
3 

3 
3 
3 
3 
8 

10 

9 

8 
7 
6 

8  40 
36 
32 
28 
24 

51  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  34  934 
9.  34  989 
9.35  044 
9.  35  099 
9.  35  154 

55 
55 
55 
55 
55 

9.  36  047 
9.36  105 
9.36  163 
9.  36  221 
9.  36  279 

0.  63  953 
0.  63  895 
0.  63  837 
0.  63  779 
0.  63  721 

9.  98  887 
9.  98  884 
9.  98  881 
9.  98  878 
9.  98  875 

5 
4 
3 
2 
1 

8  20 
16 
12 

8 
4 

52   0 

60 

9.35209 

9.36  336 

0.  63  664 

9.  98  872 

0 

8   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

t 

m.  s. 

77° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  161 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  13° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

52   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.35  209 
9.  35  263 
9.  35  318 
9.  35  373 
9.  35  427 

54 
55 
55 
54 
54 

9.36  336 
9.  36  394 
9.  36  452 
9.36  509 
9.36  566 

58 
58 
57 
57 
58 

0.  63  664 
0.63  606 
0.  63  548 
0.  63  491 
0.  63  434 

9.  98  872 
9.  98  869 
9.  98  867 
9.  98  864 
9.  98  861 

3 
2 
3 
3 
3 

60 

59 
58 
57 
56 

8   0 
56 
52 
48 
44 

52  20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  35  481 
9.  35  536 
9.  35  590 
9.35  644 
9.35  698 

55 
54 
54 
54 
64 

9.  36  624 
9.  36  681 
9.  36  738 
9.  36  795 
9.36  852 

57 
57 
57 
57 
57 

0.  63  376 
0.  63  319 
0.  63  262 
0.  63  205 
0.  63  148 

9.  98  858 
9.98855 
9.  98  852 
9.98  849 
9.  98  846 

3 
3 
3 
3 
8 

55 
54 
53 
52 
51 

7  40 
36 
32 
28 
24 

52  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  35  752 
9.35806 
9.35  860 
9.  35  914 
9.35  968 

54 
54 
54 
54 
54 

9.36  909 
9.36  966 
9.37  023 
9.  37  080 
9.37  137 

57 
57 
57 
57 
56 

0.  63  091 
0.  63  034 
0.  62  977 
0.  62  920 
0.  62  863 

9.  98  843 
9.98  840 
9.  98  837 
9.  98  834 
9.  98  831 

3 
3 
3 
3 
3 

50 

49 

48 
47 
46 

7  20 
16 
12 

8 
4 

53   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.36  022 
9.  36  075 
9.36  129 
9.36  182 
9.36  236 

53 
54 
53 
54 
53 

9.  37  193 
9.  37  250 
9.  37  306 
9.  37  363 
9.  37  419 

57 
56 
57 
56 
57 

0.  62  807 
0.  62  750 
0.  62  694 
0.  62  637 
0.  62  581 

9.  98  828 
9.  98  825 
9.  98  822 
9.  98  819 
9.  98  816 

3 
3 
3 
3 
3 

45 
44 
43 
42 
41 

7   0 
56 
52 
48 
44 

53  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  36  289 
9.36  342 
9.36  395 
9.  36  449 
9.36  502 

63 
53 
54 
53 
53 

9.  37  476 
9.  37  532 
9.37  588 
9.  37  644 
9.37  700 

56 
56 
56 
56 
66 

0.  62  524 
0.  62  468 
0.  62  412 
0.  62  356 
0.62  300 

9.  98  813 
9.  98  810 
9.  98  807 
9.  98  804 
9.  98  801 

3 
3 
3 
3 
3 

40 

39 
38 
37 
36 

6  40 
36 
32 

28 
24 

53  40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.36  556 
9.  36  608 
9.  36  660 
9.36  713 
9.36  766 

53 
52 
53 
53 
53 

9.  37  756 
9.  37  812 
9.37  868 
9.  37  924 
9.  37  980 

56 
56 
56 
56 
55 

0.  62  244 
0.  62  188 
0.  62  132 
0.  62  076 
0.62  020 

9.  98  79$ 
9.  98  795 
9.  98  792 
9.  98  789 
9.98  786 

3 
3 
3 
3 
3 

35 
34 
33 
32 
31 

6  20 
16 
12 
8 
4 

54   0 

4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  36  819 
9.  36  871 
9.36  924 
9.  36  976 
9.37  028 

52 
53 
52 
52 
53 

9.38  035 
9.38  091 
9.  38  147 
9.38  202 
9.38  257 

56 
56 
55 
55 
56 

0.61  965 
0.61  909 
0.  61  853 
0.61  798 
0.  61  743 

9.  98  783 
9.  98  780 
9.  98  777 
9.  98  774 
9.  98  771 

3 
3 
3 
3 
3 

30 

29 
28 
27 
26 

6   0 

56 
52 
48 
44 

54  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  37  081 
9.37  133 
9.37  185 
9.  37  237 
9.37  289 

52 
52 
52 
52 
52 

9.  38  313 
9.38  368 
9.  38  423 
9.  38  479 
9.  38  534 

55 
56 
66 
55 
55 

0.61  687 
0.61  632 
0.  61  577 
0.  61  521 
0.61  466 

9.  98  768 
9.98  765 
9.98  762 
9.  98  759 
9.98  756 

3 
3 
3 
3 

a 

25 
24 
23 
22 
21 

6  40 
36 
32 

28 
24 

54  40 

44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  37  341 
9.  37  393 
9.37  445 
9.  37  497 
9.  37  549 

52 
52 
52 
52 
51 

9.38  589 
9.38  644 
9.  38  699 
9.38  754 
9.38  808 

55 
55 
56 
54 
55 

0.61  411 
0.61  356 
0.61  301 
0.  61  246 
0.61  192 

9.  98  753 
9.  98  750 
9.98  746 
9.  98  743 
9.  98  740 

3 
4 
3 
3 
3 

20 

19 
18 
17 
16 

5  20 
16 
12 
8 
4 

55   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.37  600 
9.  37  652 
9.  37  703 
9.  37  765 
9.37  806 

52 
51 
52 
51 
62 

9.38  863 
9.  38  918 
9.  38  972 
9.  39  027 
9.  39  082 

55 
64 
65 
55 

54 

0.  61  137 
0.  61  082 
0.  61  028 
0.  60  973 
0.  60  918 

9.  98  737 
9.  98  734 
9.  98  731 
9.  98  728 
9.  98  725 

3 
3 
3 
3 
3 

15 
14 
13 
12 
11 

5   0 
56 
52 
48 
44 

55  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.37  858 
9.37  909 
9.37  960 
9.  38  Oil 
9.38  062 

51 
61 
51 
51 
51 

9.39  136 
9.  39  190 
9.  39  245 
9.39  299 
9.  39  353 

54 
55 
54 
54 
54 

0.  60  864 
0.  60  819 
0.  60  755 
0.  60  701 
0.60  647 

9.98  722 
9.  98  719 
9.  98  715 
9.  98  712 
9.  98  709 

3 
4 
3 
3 
3 

10 

9 
8 
7 
6 

4  40 
36 
32 
28 
24 

55  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.  38  113 
9.38  164 
9.  38  215 
9.  38  266 
9.  38  317 

51 
51 
51 
51 
51 

9.  39  407 
9.  39  461 
9.  39  515 
9.  39  569 
9.  39  623 

64 
54 
54 
54 

54 

0.  60  593 
0.  60  539 
0.60  485 
0.  60  431 
0.  60  377 

9.  98  706 
9.98  703 
9.  98  700 
9.  98  697 
9.  98  694 

3 
3 
3 
3 
4 

5 
4 
3 
2 
1 

4  20 
16 
12 
8 
4 

56   0 

60 

9.38  368 

9.  39  677 

0.  60  323 

9.  98  690 

0 

4   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

46061—08 11 


76° 


162 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
Oh  14° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

56   0 
4 
8 
12 
16 

0 

1 

2 

3 

4 

9.  38  368 
9.  38  418 
9.  38  469 
9.  38  519 
9.  38  570 

50 
51 
50 
51 

9.  39  677 
9.  39  731 
9.39  785 
9.  39  838 
9.  39  892 

54 
54 
53 
54 

0.  60  323 
0.  60  2G9 
0.  60  215 
0.  60  162 
0.  60  108 

9.  98  690 
9.  98  687 
9.98  684 
9.  98  681 
9.  98  678 

3 
3 
3 
3 

60 

59 
58 
57 
56 

4   0 
56 
52 
48 
44 

56  20 
24 
28 
32 
36 

5 
6 

8 
9 

9.38  620 
9.  38  670 
9.38  721 
9.38  771 
9.38  82  L 

50 
51 
50 
50 
50 

9.  39  945 
9.  39  999 
9.  40  052 
9.40  106 
9.  40  159 

54 
53 
54 
53 
53 

0.  60  055 
0.60  001 
0.  59  948 
0.  59  894 
0.  59  841 

9.  98  675 
9.  98  671 
9.  98  668 
9.  98  665 
9.  98  662 

4 
3 
3 
3 

55 
54 
53 
52 
51 

3  40 
36 
32 
28 
24 

56  40 
44 
48 
52 
56 

10 

11 

12 
13 
14 

9.  38  87J 
9.  38  921 
9.  38  971 
9.  39  021 
9.  39  071 

50 
50 
50 
50 
50 

9.40  212 
9.  40  266 
9.  40  319 
9.  40  372 
9.40  425 

54 
53 
53 
53 

KO 

0.59  788 
0.  59  734 
0.  59  681 
0.59  628 
0.  59  575 

9.  98  659 
9.  98  656 
9.  98  652 
9.  98  649 
9.  98  646 

3 
4 
3 
3 

50 

49 
48 
47 
46 

3  20 
16 
12 
8 
4 

57   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  39  121 
9.  39  170 
9.39  220 
9.  39  270 
9.  39  319 

49 
50 
50 
49 

KA 

9.  40  478 
9.40  531 
9.40  584 
9.  40  636 
9.  40  689 

53 
53 
52 
53 

^q 

0.  59  522 
0.  59  469 
0.  59  416 
0.  59  364 
0.  59  311 

9.  98  643 
9.  98  640 
9.  98  636 
9.  98  633 
9.  98  630 

3 
4 
3 
3 

45 
44 
43 
42 
41 

3   0 

56 
52 

48 
44 

57  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.39  369  j 
'  9.  39  418 
9.  39  467 
9.  39  517 
9.  39  566 

49 
49 
50 
49 
49 

9.  40  742 
9.  40  795 
9.  40  847 
9.40  900 
9.  40  952 

53 
52 
53 
52 
53 

0.  59  258 
0.  59  205 
0.  59  153 
0.  59  100 
0.59  048 

9.  98  627 
9.  98  623 
9.  98  620 
9.  98  617 
9.  98  614 

4 
3 
3 
3 

40 

39 
38 
37 
36 

2  40 
36 
32 

28 
24 

57  40 
44 
48 
52 
56 

25 
26 

27 
28 
29 

9.  39  615 
9.  39  664 
9.  39  713 
9.  39  762 
9.  39  811 

49 
49 
49 
49 
49 

9.41  005 
9.41  057 
9.  41  109 
9.41  161 
9.  41  214 

52 
52 
52 
53 
52 

0.  58  995 
0.58  943 
0.  58  891 
0.  58  839 
0.  58  786 

9.  98  610 
9.  98  607 
9.  98  604 
9.  98  601 
9.  98  597 

3 
3 

3 
4 

35 
34 
33 
32 
31 

2  20 
16 
12 

8 
4  , 

58   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  39  860 
9.39909 
9.  39  958 
9.40  006 
9.40  055 

49 
49 

48 
49 
48 

9.  11  266 
9.41  318 
9.  41  370 
9.  41  422 
9.  41  474 

52 
52 
52 
52 
52 

0.  58  734 
0.58  682 
0.58  630 
0.  58  578 
0.  58  526 

9.  98  594 
9.98  591 
9.98  588 
9.  98  584 
9.  98  581 

3 
3 
4 
3 

30 

29 
28 
27 
26 

2   0 
56 
52 
48 
44 

58  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  40  103 
9.  40  152 
9.40  200 
9.  40  249 
9.40  297 

49 
48 
49 
48 
49 

9.41  526 
9.41  578 
9.41  629 
9.  41  681 
9.41  733 

52 
51 
52 
52 
51 

0.  58  474 
0.  58  422 
0.  58  371 
0.  58  319 
0.  58  267 

9.  98  578 
9.  98  574 
9.  98  571 
9.  98  568 
9.98  565 

4 
3 
3 
3 

25 
24 
23 
22 
21 

1  40 
36 
32 

28 
24 

58  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  40  346 
9.40394 
9.  40  442 
9.  40  490 
9.  40  538 

48 
48 
48 
48 
48 

9.  41  784 
9.41  836 
9.  41  887 
9.41  939 
9.41  990 

52 
51 
52 
51 
51 

0.58  216 
0.58  164 
0.  58  113 
0.  58  061 
0.  58  010 

9.98  561 
9.  98  558 
9.  98  555 
9.  98  551 
9.  98  548 

3 
3 
4 
3 
3 

20 

19 
18 
17 
16 

1  20 
16 
12 
8 
4 

59   0 
4 

8 
12 
16 

45 
46 
47 
48 
49 

9.  40  586 
9.  40  634 
9.  40  682 
9.40  730 
9.40  778 

48 
48 
48 
48 
47 

9.  42  041 
9.  42  093 
9.42  144 
9.42  195 
9.  42  246 

52 
51 
51 
51 
51 

0.  57  959 

0.  57  907 
0.  57  866 
0.57  805 
0.  57  754 

9.98  545 
9.98  541 
9.  98  538 
9.  98  535 
9.  98  531 

4 
3 
3 
4 
3 

15 
14 
13 
12 
11 

1   0 
56 
52 
48 
44 

59  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.40825 
9.  40  873 
9.  40  921 
9.40  968 
9.41  016 

48 
48 
47 
48 
47 

9.  42  297 
9.42  348 
9.  42  399 
9.42  450 
9.  42  501 

51 
51 
51 
51 
51 

0.  57  703 
0.57  652 
0.57  601 
0.  57  550 
0.  57  499 

9.  98  528 
9.  98  525 
9.  98  521 
9.  98  518 
9.98  515 

3 
4 
3 
3 
4 

10 

9 

8 

6 

0  40 
36 
32 

28 
24 

59  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.41  063 
9.41  111 
9.41  158 
9.41  205 
9.41  252 

48 
47 
47 
47 
48 

9.42  552 
9.  42  603 
9.  42  653 
9.42  704 
9.  42  755 

51 
50 
51 
51 
50 

0.57  448 
0.57  397 
0.57  347 
0.  57  296. 
0.  57  245 

9.  98  511 
9.  98  508 
9.  98  505 
9.  98  501 
9.  98  498 

3 
3 
4 
3 
4 

5 
4 
3 
2 
1 

0  20 
16 
12 
8 
4 

60   0 

60 

9.41  300 

9.42  805 

0.  57  195 

9.  98  494 

0 

0   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

75° 


5h 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


163 


TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  15° 


m.  s. 

• 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

0    0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.41  300 
9.41  347 
9.  41  394 
9.41  441 
9.  41  488 

47 
47 
47 
47 

9.  42  805 
9.42  856 
9.42  906 
9.  42  957 
9.43007 

51 

50 
51 
50 

0.  57  195 
0.  57  144 
0.  57  094 
0.  57  043 
0.56  993 

9.  98  494 
9.  98  491 

9.98488 
9.  98  484 
9.  98  481 

3 
3 
4 
3 

60 

59 
58 
57 
56 

60   0 
56 
52 
48 
44 

0   20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.41  535 
9.41  582 
9.41  628 
9.41  675 
9.41  722 

47 
46 
47 
47 

9.  43  057 
9.  43  108 
9.  43  158 
9.  43  208 
9.  43  258 

51 
50 
50 
50 

0.56  943 
0.  56  892 
0.56  842 
0.56  792 
0.56  742 

9.  98  477 
9.  98  474 
9.  98  471 
9.  98  467 
9.  98  464 

3 
3 
4 
3 

55 
54 
53 
52 
51 

59   40 
36 
32 
28 
24 

0   40 
44 

48 
53 
56 

10 

11 
12 
13 
14 

9.41  768 
9.  41  815 
9.  41  861 
9.41  908 
9.41  954 

47 
46 
47 
46 

9.  43  308 
9.  43  358 
9.  43  408 
9.  43  458 
9.43508 

50 
50 
50 
50 

0.56  692 
0.  56  642 
0.56  592 
0.56  542 
0.  56  492 

9.98460 
9.  98  457 
9.98  453 
9.  98  450 
9.  98  447 

3 
4 
3 
3 

50 

49 
48 
47 
46 

59   20 
16 
12 

8 
4 

1    0 
4 

8 
12 
16 

15 
16 
17 

18 
19 

9.42  001 
9.  42  047 
9.  42  093 
9.42  140 
9.  42  186 

46 
46 
47 
46 

9.43  558 
9.43  607 
9.43  657 
9.  43  707 
9.43  756 

49 
50 
50 
49 

0.  56  442 
0.  56  393 
0.56  343 
0.  56  293 
0.  56  244 

9.98443 
9.  98  440 
9.  98  436 
9.  98  433 
9.  98  429 

3 
4 
3 

4 

45 
44 
43 
42 
41 

59   0 
56 
52 
48 
44 

1   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.42  232 
9.  42  278 
9.  42  324 
9.  42  370 
9.  42  416 

46 
46 
46 
46 

9.43  806 
9.  43  855 
9.43  905 
9.  43  954 
9.44  004 

49 
50 
49 
50 

0.5C  194 
0.56  145 
0.  56  095 
0.  56  046 
0.  55  996 

'.».  '.IS  426 
9.  98  422 
9.  98  419 
C.  98  415 
9.  <*5.  412 

4 

3 
4 
3 

40 

39 
38 
37 
36 

58   40 
36 
32 

28 
24 

1   40 
44 

48 
52 
56 

25 
26 
27 

28 
29 

9.  42  461 
9.  42  507 
9.42  553 
9.  42  599 
9.  42  644 

46 
46 
46 
45 

9.44053 
9.  44  102 
9.  44  151 
9.44  201 
9.44  250 

49 
49 
50 
49 

0.  55  947 
0.  55  898 
0.  55  849 
0.55  799 
0.  55  750 

9.98409 
9.  98  405 
9.  98  402 
9.  98  398 
9.  98  395 

4 
3 
4 
3 

35 
34 
33 
32 
31 

58   20 
16 
12 

8 
4 

2  I 

8 
12 
16 

30 

31 
32 
33 
34 

9.  42  690 
9.  42  735 
9.  42  781 
9.  42  826 
9.  42  872 

45 
46 
45 
46 

9.44  299 
9.44  348 
9.44  397 
9.  44  446 
9.  44  495 

49 

49 
49 
49 

0.  55  701 
0.  55  652 
0.55  603 
0.  55  554 
0.  55  505 

9.  98  391 

9.  98  388 
9.98  384 
9.  98  381 
9.  98  377 

3 
4 
3 

4 

30 

29 

28 
27 
26 

58   0 
56 

52 
48 
44 

2   20 
24 
28 
32 
36 

35 

36 
37 
38 
39 

9.  42  917 
9.  42  962 
9.  43  008 
9.  43  053 
9.  43  098 

45 
46 
45 
45 

9.  44  544 
9.  44  592 
9.44  641 
9.44  690 
9.  44  738 

48 
49 
49 

48 

0.  55  456 
0.  55  408 
0.  55  359 
0.  55  310 
0.  55  262 

9.  98  373 
9.98  370 
9.98  366 
9.98  363 
9.  98  359 

3 

4 
3 
4 

25 
24 
23 
22 
21 

57   40 
36 
32 

28 
24 

2   40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  43  143 
9.  43  188 
9.  43  233 
9.  43  278 
9.43  323 

45 
45 
45 
45 

9.  44  787 
9.44  836 
9.44  884 
9.  44  933 
9.  44  981 

49 

48 
49 

48 

0.  55  213 

0.  55  164 
0.  55  116 
0.  55  067 
0.55  019 

9.  98  356 
9.  98  352 
9.  98  349 
9.  98  345 
9.  98  342 

4 
3 
4 
3 

20 

19 

18 
'  17 
16 

57   20 
16 
12 

8 
4 

3    0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.  43  367 
9.43  412 
9.  43  457 
9.43502 
9.  43  546 

45 
45 
45 
44 

9.45  029 
9.  45  078 
9.45  126 
9.45  174 
9.  45  222 

49 

48 
48 
48 

0.54  971 
0.54  922 
0.54  874 
0.  54  826 
0.  54  778 

9.  98  338 
9.98  334 
9.  98  331 
9.98  327 
9.  98  324 

4 
3 
4 
3 

15 
14 
13 
12 
11 

57   0 
56 
52 
48 
44 

3   20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.  43  591 
9.43  635 
9.43  680 
9.43  724 
9.  43  769 

44 
45 

44 
45 

9.45271 
9.45  319 
9.45  367 
9.45  415 
9.  45  463 

48 
48 
48 
48 

0.  54  729 
0.  54  681 
0.  54  633 
0.54  585 
0.  54  537 

9.  98  320 
9.  98  317 
9.  98  313 
9.  98  309 
9.  98  306 

3 
4 
4 
3 

10 

9 

8 
7 
6 

56   40 
36 
32 

28 
24 

3   40 
44 

48 
52 
56 

:>:. 
56 
57 
58 
59 

9.  43  813 
9.  43  857 
9.  43  901 
9.  43  946 
9.43  990 

44 
44 
45 
44 

9.45  511 
9.  45  559 
9.  45  606 
9.  45  654 
9.  45  702 

48 
47 
48 
48 

0.  54  489 
0.  54  441 
0.  54  394 
0.54  346 
0.  54  298 

9.  98  302 
9.  98  299 
9.  98  295 
9.98  291 
9.  98  288 

3 

4 
4 
3 

5 

4 
3 

2 

1 

56   20 
16 
12 
8 
4 

4    0 

60 

9.  44  034 

9.  45  750 

0.54  250 

9.  98  284 

0 

56   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.   s. 

74c 


164  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  16° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

4   0 
4 
8 
12 
16 

0 

1 

2 
3 
4 

9.  44  034 
9.  44  078 
9.  44  122 
9.  44  166 
9.  44  210 

44 
44 
44 
44 
43 

9.45  750 
9.  45  797 
9.  45  845 
9.45  892 
9.45  940 

47 
48 
47 
48 
47 

0.54  250 
0.  54  203 
0.54  155 
0.  54  108 
0.  54  060 

9.  98  284 
9.  98  281 
9.  98  277 
9.  98  273 
9.  98  270 

3 
4 
4 
3 
4 

60 

59 
58 
57 
56 

56   0 
56 
52 
48 
44 

4  20 

24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  44  253 
9.44  297 
9.  44  341 
9.44  385 
9.44  428 

44 
44 
44 
43 
44 

9.  45  987 
9.46  035 
9.  46  082 
9.  46  130 
9.46  177 

48 
47 
48 
47 
47 

0.  54  013 
0.  53  965 
0.  53  918 
0.  53  870 
0.  53  823 

9.  98  266 
9.  98  262 
9.98  259 
9.  98  255 
9.  98  251 

4 
3 
4 

4 
3 

55 
54 
53 
52 
51 

55  40 
36 
32 
28 
24 

4  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  44  472 

9.  44  516 
9.  44  559 
9.  44  602 
9.  44  646 

44 
43 
43 
44 
43 

9.  46  224 
9.  46  271 
9.  46  319 
9.  46  366 
9.46  413 

47 
48 
47 
47 
47 

0.  53  776 
0.  53  729 
0.  53  681 
0.  53  634 
0.  53  587 

9.  98  248 
9.  98  244 
9.98  240 
9.  98  237 
9.  98  233 

4 
4 
3 
4 
4 

50 

49 
48 
47 
46 

55  20 
16 
12 
8 
4 

5   0 
4 

8 
12 
16 

15 
16 
17 
18 
19 

9.44  689 
9.  44  733 
9.  44  776 
9.  44  819 
9.  44  862 

44 
43 
43 
43 
43 

9.  46  460 
9.46  507 
9.  46  554 
9.  46  601 
9.  46  648 

47 
47 

47 
47 
46 

0.  53  540 
0.  53  493 
0.  53  446 
0.  53  399 
0.  53  352 

9.  98  229 
9.  98  226 
9.  98  222 
9.  98  218 
9.  98  215 

3 
4 
4 
3 

4 

45 
44 
43 
42 
41 

55   0 
56 
52 
48 
44 

5  20 

24 
28 
82 
36 

•_>o 

21 
22 
23 
24 

9.44  905 
9.  44  948 
9.44  992 
9.  45  035 
9.  45  077 

43 
44 
43 
42 
43 

9.  46  694 
9.46  741 
9.  46  788 
9.  46  835 
9.  46  881 

47 
47 
47 
46 
47 

0.  53  306 
0.  53  259 
0.  53  212 
0.  53  165 
0.  53  119 

9.  98  211 
9.  98  207 
9.  98  204 
9.  98  200 
9.  98  1% 

4 
3 
4 
4 
4 

40 

39 
38 
37 
36 

54  40 
36 
32 
28 
24 

5  40 
44 

48 
52 
56 

25 
26 
27 
28 
29 

9.  45  120 
9.45  163 
9.45  206 
9.  45  249 
9.  45  292 

43 
43 
43 
43 
42 

9.46  928 
9.  46  975 
9.47  021 
9.47  068 
9.47  114 

47 

•  46 
47 
46 
46 

0.  53  072 
0.  53  025 
0.  62  979 
0.  52  932 
0.  52  886 

9.98  192 
9.98  189 
9.98  185 
9.98  181 
9.98  177 

3 
4 

4 

4 

s 

35 
34 
33 
32 
31 

54  20 
16 
12 
8 
4 

6   0 
4 

8 
12 
16 

30 

31 
32 
33 
34 

9.  45  334 
9.  45  377 
9.  45  419 
9.  45  462 
9.45  504 

43 
42 
43 
42 
43 

9.47  160 
9.  47  207 
9.  47  253 
9.47  299 
9.  47  346 

47 
46 
46 
47 
46 

0.  52  840 
0.  52  793 
0.52  747 
0.  52  701 
0.  02  654 

9.  98  174 
9.98  170 
9.  98  166 
9.98  162 
9.  98  159 

4 
4 
4 
3 

4 

30 

29 
28 
27 
26 

54   0 

56 
52 
48 
44 

6  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  45  547 
9.45  589 
9.  45  632 
9.  45  674 
9.  45  716 

42 
43 
42 
42 
42 

9.  47  392 
9.47  438 
9.  47  484 
9.  47  530 
9.  47  576 

46 
46 
46 
46 
46 

0.  52  608 
0.  62  562 
0.  52  516 
0.  52  470 
0.  52  424 

9.  98  155 
9.  98  151 
9.  98  147 
9.  98  144 
9.  98  140 

4 
4 
3 
4 
4 

25 
24 
23 
22 
21 

53  40 
36 
32 
28 
24 

6  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.45  758 
9.  45  801 
9.  45  843 
9.  45  885 
9.  45  927 

43 

42 
42 
42 
42 

9.  47  622 
9.47  668 
9.47  714 
9.47  760 
9.47  806 

46 
46 
46 
46 
46 

0.  52  378 
0.  52  332 
0.  52  286 
0.  52  240 
0.  52  194 

9.  98  136 
9.98  132 
9.  98  129 
9.98  125 
9.  98  121 

4 
3 
4 
4 
4 

20 

19 
18 
17 
16 

53  20 
16 
12 

8 
4 

7   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

9.  45  969 
9.46  Oil 
9.46  053 
9.  46  095 
9.  46  136 

42 
42 
42 
41 
42 

9  47  852 
9.  •»?  897 
9  47  943 
9.  47  989 
9.  4^  035 

45 
46 
46 
46 
45 

0.  52  148 
0.52  103 
0.52  057 
0.52  Oil 
0.51  965 

9.98  117 
9.  98  113 
9.98  110 
9.  98  106 
9.98  102 

4 
3 

4 
4 
4 

15 
14 
13 
12 
11 

53   0 
56 
52 
48 
44 

7  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.46  178 
9.  46  220 
9.  46  262 
9.  46  303 
9.  46  345 

42 
42 
41 
42 
41 

9.  48  080 
9.48  126 
9.  58  171 
9.  48  217 
9.  48  262 

46 
45 
46 
45 
45 

0.51  920 
0.51  874 
0.51  829 
0.51  783 
0.51  738 

9.  98  098 
9.98  094 
9.  98  090 
9.  98  087 
9.  98  083 

4 
4 
3 
4 
4 

10 

9 

8 

6 

52  40 
36 
32 
28 
24 

7  40 

"44 
48 
52 
56 

55 

56 
57 
58 
59 

9.46  386 
9.  46  428 
9.  46  469 
9.  4"6  511 
9.  46  552 

42 
41 
42 
41 
42 

9.  48  307 
9.48  353 
9.48  398 
9.  48  443 
9.  48  489 

46 
45 
45 
46 
45 

0.51  693 
0.51  647 
0.  51  602 
0.51  557 
0.51  511 

9.  98  079 
9.  98  075 
9.  98  071 
9.  98  067 
9.  98  063 

4 
4 
4 
4 
3 

5 
4 
3 

1 

52  20 
16 
12 
8 
4 

8   0 

60 

9.  46  694 

9.  48  534 

0.51  466 

9.  98  060 

0 

,T2   0 

L.  Cos 

d. 

L.  Cotg. 

c.d. 

L.  Tang 

L.  Sin. 

d. 

' 

m.  s. 

73° 


GEOGRAPHIC    TABLES    AND   FORMULAS.  165 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  17° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

a. 

8   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  46  594 
9.46  635 
9.46  676 
9.  46  717 
9.46  758 

41 
41 
41 
41 
42 

9.48  534 
9.48  579 
9.  48  624 
9.48  669 
9.  48  714 

45 
45 
45 
45 
45 

0.51  466 
0.51  421 
0.51  376 
0.51  331 
0.  51  286 

9.  98  060 
9.  98  056 
9.98  052 
9.  98  048 
9.  98  044 

4 
4 
4 
4 
4 

60 

59 
58 
57 
56 

52   0 
56 
52 
48 
44 

8  20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.46  800 
9.  46  841 
9.  46  882 
9.46  923 
9.46  964 

41 
41 
41 
41 
41 

9.  48  759 
9.48  804 
9.  48  849 
9.  48  894 
9.  48  939 

45 
45 
45 
45 

45 

0.  61  241 
0.51  196 
0.51  151 
0.  51  106 
0.  51  061 

9.  98  040 
9.  98  036 
9.  98  032 
9.  98  029 
9.  98  025 

4 
4 
3 
4 
4 

55 
54 
53 
52 
51 

51  40 
36 
32 
28 
24 

8  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.47  005 
9.47  045 
9.47  086 
9.47  127 
9.47  168 

40 
41 
41 
41 
41 

9.  48  984 
9.  49  029 
9.  49  073 
9.49  118 
9.  49  163 

45 
44 
45 
45 

44 

0.51  016 
0.  50  971 
0.  50  927 
0.  50  882 
0.50  837 

9.  98  021 
9.98017 
9.  98  013 
9.  98  009 
9.98  005 

4 
4 
4 
4 
4 

50 

49 
48 
47 
46 

51  20 
16 
12 

8 
4 

9   0 
4 
8 
•12 

16 

15 
16 
17 
18 
19 

9.  47  209 
9.  47  249 
9.  47  290 
9.47  330 
9.47  371 

40 
41 
40 
41 
40 

9.49  207 
9.  49  252 
9.  49  296 
9.49  341 
9.49  385 

45 
44 
45 
44 
45 

0.  50  793 
0.  50  748 
0.50  704 
0.  50  659 
0.  50  615 

9.  98  001 
9.  97  997 
9.  97  993 
9.97  989 
9.97  986 

4 
4 
4 
3 
4 

45 
44 
43 

42T 
41 

51   0 
56 
52 
48 
44 

9  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  47  411 
9.  47  452 
9.  47  492 
9.  47  533 
9.  47  573 

41 
40 
41 
40 
40 

9.  49  430 
9.  49  474 
9.  49  519 
9.49  563 
9.  49  607 

44 
45 
44 
44 
45 

0.  50  570 
0.  50  526 
0.  50  481 
0.  50  437 
0.  50  393 

9.  97  982 
9.  97  978 
9.  97  974 
9.  97  970 
9.  97  966 

4 
4 
4 
4 
4 

40 

39 
38 
37 
36 

50  40 
36 
32 
28 
24 

9  40 
44 
48 
52 
56 

25 

26 
27 
28 
29 

9.  47  613 
9.47  654 
9.47  694 
9.  47  734 
9.  47  774 

41 
40 
40 
40 
40 

9.49  652 
9.49  696 
9.  49  740 
9.  49  784 
9.  49  828 

44 
44 
44 
44 
44 

0.  50  348 
0.  50  304 
0.50  260 
0.  50  216 
0.  50  172 

9.  97  962 
9.  97  958 
9.  97  954 
9.  97  950 
9.  97  946 

4 
4 
4 
4 
4 

35 
34 
33 
32 
31 

50  20 
16 
12 

8 
4 

10   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.47  814 
9.47  854 
9.  47  894 
9.  47  934 
9.47  974 

40 
40 
40 
40 
40 

9.  49  872 
9.49  916 
9.  49  960 
9.50  004 
9.50048 

44 
44 
44 
44 

44 

0.50  128 
0.50  084 
0.  50  040 
0.  49  996 
0.  49  952 

9.97  942 
9.  97  938 
9.97  934 
9.97  930 
9.  97  926 

4 
4 
4 
4 
4 

30 

29 
28 
27 
25 

50   0 
50 
52 
48 
44 

10  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  48  014 
9.48  054 
9.48  094 
9.48  133 
9.48  173 

40 
40 
39 
40 
40 

9.50  092 
9.50  136 
9.50  180 
9.50  223 
9.50  267 

44 
44 
43 
44 
44 

0.  49  908 
0.49  864 
0.  49  820 
0.49  777 
0.49  733 

9.  97  922 
9.  97  918 
9.  97  914 
9.  97  910 
9.97  906 

4 
4 
4 
4 
4 

25 

24 
23 
22 
21 

I'.i  Hi 
36 
32 
28 
24 

10  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.48  213 
9.  48  252 
9.48  292 
9.  48  332 
9.48371 

39 
40 
40 
39 
40 

9.50311 
9.50  355 
9.  50  398 
9.50  442 
9.50  485 

44 
43 
44 
43 
44 

0.49  689 
0.  49  645 
0.  49  602 
0.49  558 
0.  49  515 

9.  97  902 
9.  97  898 
9.  97  894 
9.97  890 
9.  97  886 

4 

•20 

19 
18 
17 
16 

49  20 
16 
12 

8 

1 

11   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.48  411 
9.  48  450 
9.  48  490 
9.48  529 
9.48  568 

39 
40 
39 
39 
39 

9.50  529 
9.  50  572 
9.50  616 
9.  50  659 
9.  50  703 

44 
44 
43 
44 
43 

0.  49  471 
0.  49  428 
0.  49  384 
0.  49  341 
0.  49  297 

9.  97  882 
9.  97  878 
9.  97  874 
9.  97  870 
9.  97  866 

4 
5 

1f> 
14 
13 
12 
11 

49   0 
56 
52 
48 
44 

11  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  48  607 
9.  48  647 
9.48  686 
9.  48  725 
9.48  764 

40 
39 
39 
39 
39 

9.50  746 
9.  50  789 
9.  50  833 
9.50876 
9.  50  919 

43 
44 
43 
43 
43 

0.  49  254 
0.  49  211 
0.49  167 
0.49  124 
0.  49  081 

9.  97  861 
9.  97  857 
9.  97  853 
9.  97  849 
9.  97  845 

4 
4 
4 

4 

10 

9 

8 
7 
6 

IS  .10 
36 
32 
28 
24 

11  40 
44 

48 
52 
56 

55 

56 
57 
58 
59 

9.48  803 
9.  48  842 
9.  48  881 
9.48  920 
9.  48  959 

39 
39 
39 
39 
39 

9.50  962 
9.51  005 
9.  51  048 
9.  51  092 
9.  51  135 

43 
43 
44 
43 
43 

0.  49  038 
0.  48  995 
0.  48  952 
0.  48  908 
0.  48  865 

9.  97  841 
9.  97  837 
9.  97  833 
9.  97  829 
9.  97  825 

4 

4 
4 
4 

5 
4 
3 
2 
1 

48  20 
16 
12 
8 
4 

12   0 

60 

9.  48  998 

9.51  178 

0.  48  822 

9.97  821 

0 

48   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

72° 


166  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc, — Continued. 

lh  18° 


m.  s. 

t 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

12   0 
4 
8 
12 
16 

0 

1 
2 

3 
4 

9.  48  998 
9.  49  037 
9.49  076 
9.  49  115 
9.  49  153 

39 
39 
39 

38 
39 

9.  51  178 
9.51  221 
9.  51  264 
9.  51  306 
9.51  349 

43 
43 
42 
43 
43 

0.  48  822 
0.48  779 
0.  48  736 
0.  48  694 
0.  48  651 

9.  97  821 
9.  97  817 
9.  97  812 
9.  97  808 
9.  97  804 

4 
5 
4 
4 
4 

60 

59 
58 
57 
56 

48   0 
56 
52 
48 
44 

12  20 
24 
28 
32 
36 

5 

6 
7 

8 
9 

9.49  192 
9.  49  231 
9.  49  269 
9.  49  308 
9.  49  347 

39 
38 
39 
39 

38 

9.  51  392 
9.  51  435 
9.51  478 
9.51  520 
9.  51  563 

43 
43 
42 
43 
43 

0.  48  608 
0.  48  565 
0.  48  522 
0.  48  480 
0.  48  437 

9.97  800 
9.97  796 
9.  97  792 
9.  97  788 
9.  97  784 

4 
4 
4 
4 
5 

55 
54 
53 
52 
51 

47  40 
36 
32 

28 
24 

12  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.49  385 
9.  49  424 
9.  49  462 
9.  49  500 
9.  49  539 

39 
38 
38 
39 

38 

9.  51  606 
9.51  648 
9.  51  691 
9.51  734 
9.51  776 

42 
43 
43 
42 
43 

0.  48  394 
0.  48  352 
0.48  309 
0.  48  266 
0.  48  224 

9.  97  779 
9.  97  775 
9.  97  771 
9.  97  767 
9.  97  763 

4 
4 
4 
4 
4 

50 

49 
48 
47 
46 

47  20 
16 
12 
8 
4 

13   0 
4 
8 
12 
16 

15 
16 
17 
^•18 
19 

9.  49  577 
9.  49  615 
9.  49  654 
9.  49  692 
9.  49  730 

38 
39 
38 

38 
38 

9.51  819 
9.  51  861 
9.  51  903 
9.51  946 
9.  51  988 

42 
42 
43 
42 
43 

0.  48  181 
0.48  139 
0.  48  097 
0.  48  054 
0.  48  012 

9.  97  759 
9.  97  754 
9.  97  750 
9.97  746 
9.  97  742 

5 
4 
4 
4 
4 

45 
44 
43 
42 
41 

47   0 
56 
52 
-   48 
44 

13  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  49  768 
9.  49  806 
9.  49  844 
9.  49  882 
9.  49  920 

38 
38 
38 
38 
38 

9.  52  031 
9.  52  073 
9.  52  115 
9.  52  157 
9.52  200 

42 
42 
42 
43 
42 

0.  47  969 
0.  47  927 
0.  47  885 
0.  47  843 
0.  47  800 

9.  97  738 
9.97  734 
9.  97  729 
9.  97  725 
9.  97  721 

4 
5 
4 
4 
4 

40 

39 
38 
37 
36 

46  40 
36 
32 
28 
24 

13  40 

44 
48 
52 
56 

25 
26 

27 
28 
29 

9.  49  958 
9.  49  996 
9.  £0  034 
'.).  f  0  072 
9.  50  110 

38 
38 
38 
38 
38 

9.  52  242 

9.  52  284 
9.  52  326 
9.  52  368 
9.  52  410 

42 

42 
42 
42 
42 

0.47  758 
0.  47  716 
0.47  674 
0.  47  632 
0.47  590 

9.  97  717 
9.  97  713 

9.  97  708 
9.  97  704 
9.  97  700 

4 
5 
4 
4 
4 

35 
34 
33 
32 
31 

46  20 
16 
12 

8 
4 

14   0 
4 
8 
12 
16 

30 
81 

32 
33 
34 

9.  50  148 
9.  50  185 
9.  50  223 
9.  50  261 
9.  50  298 

37 
38 
38 
37 
38 

9.  52  452 
9.  52  494 
9.  52  536 
9.  52  578 
9.  52  620 

42 
42 
42 
42 
41 

0.  47  548 
0.47  506 
0.  47  464 
0.47  422 
0.  47  380 

9.  97  696 
9.  97  691 
9.97  687 
9.97  683 
9.  97  679 

5 
4 
4 
4 
5 

30 

29 

28 
27 
26 

46   0 
56 
52 

48 
44 

14  20 
21 

28 
32 
36 

35 
36 
37 
38 
39 

9.  50  336 
9.  50  374 
9.  50  411 
9.  *  0  449 
9.  50  486 

38 
37 
38 
37 
37 

9.  52  661 
9.  52  703 
9.52  745 
9.  52  787 
9.  52  829 

42 
42 
42 
42 
41 

0.  47  339 
0.  47  297 
0.  47  255 
0.47  213 
0.47  171 

«.>.  it?  <;:  i 

9.  97  670 
9.  97  666 
9.  97  662 
9.  97  657 

4 
4 
4 
5 
4 

25 
24 
23 
22 
21 

45  40 
36 
32 
28 
24 

14  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  50  523 
9.  50  561 
9.  50  598 
9.  50  635 
9.  50  673 

38 
37 
37 
38 
37 

9.  52  870 
9.  52  912 
9.  52  95? 
9.52  995 
9.  53  037 

42 
41 
42 
42 
41 

0.  47  130 
0.47  088 
0.47  047 
0.  47  C05 
0.  46  963 

9.97  653 
9.97  649 
9.  97  645 
9.  97  640 
9.  97  636 

4 
4 
5 
4 
4 

20 

19 
18 
17 
16 

45  20 
16 
12 
8 
4 

15   0 
4 
8 
12 
16 

45 
46 
47 
48 

49 

9.  50  710 
9.  50  747 
9.  50  784 
9.  50  821 
9.50858 

37 
37 
37 
37 
38 

9.53  078 
9.53  120 
9.  53  161 
9.  53  202 
9.  53  244 

42 
41 
41 

42 
41 

0.  46  922 
0.  46  880 
0.  46  839 
0.46  798 
0.  46  756 

9.  97  632 
9.97  628 
9.  97  623 
9.  97  619 
9.  97  615 

4 
5 
4 
4 
5 

15 
14 
13 
12 
11 

45   0 
56 
52 
48 
44 

15  20 

24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  50  896 
9.  50  933 
9.  50  970 
9.  51  007 
9.  51  043 

37 
37 
37 
36 
37 

9.  53  285 
9.  53  327 
9.  53  368 
9.53  409 
9.53450 

42 
41 
41 
41 

42 

0.  46  715 
0.  46  673 
0.  46  632 
0.  46  591 
0.  46  550 

9.  97  610 
9.  97  606 
9.  97  602 
9.  97  597 
9.  97  593 

4 
4 
5 
4 

4 

10 

9 

8 
7 
6 

44  40 
36 
32 
28 
24 

15  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.51  080 
9.  51  117 
9.51  154 
9.  51  191 
9.  51  227 

37 
37 
37 
36 
37 

9.  53  492 
9.  53  533 
9.  53  5  4 
9.  53  615 
9.  53  656 

41 
41 
41 
41 
41 

0.  46  508 
0.46467 
0.  46  426 
0.  46  385 
0.  46  344 

9.  97  589 
9.  97  584 
9.  97  580 
9.  97  576 
9.  97  571 

5 
4 
4 

5 
4 

5 
4 
3 
2 
1 

44  20 
16 
12 
8 
4 

16   0 

60 

9.  51  264 

9.  53  697 

0.  46  303 

9.97  567 

0 

44   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

71° 


GEOGRAPHIC    TABLES    AND   FORMULAS.  167 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  19° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

16   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  51  264 
9.  51  301 
9.  51  338 
9.  51  374 
9.  51  411 

37 
37 
36 
37 
36 

9.  53  697 
9.53  738 
9.  53  779 
9.53  820 
9.  53  861 

41 
41 
41 
41 
41 

0.  46  303 
0.  46  262 
0.46  221 
0.  46  180 
0.  46  139 

9.  97  567 
9.  97  563 
9.  97  558 
9.  97  554 
9.  97  550 

4 
5 
4 

4 
5 

60 

59 
58 
57 
56 

44   0 
56 
52 
48 
44 

16  20 
24 
28 
32 
36 

5 

6 
7 
8 
9 

9.51  447 
9.  51  484 
9.  51  520 
9.51  557 
9.51  593 

37 
36 
37 
36 
36 

9.53  902 
9.  53  943 
9.  53  984 
9.  54  025 
9.54065 

41 
41 
41 
40 
41 

0.46  098 
0.  46  057 
0.  46  016 
0.  45  975 
0.45  935 

9.97  545 
9.  97  541 
9.  97  536 
9.  97  532 
9.  97  528 

4 
5 

4 
4 
5 

55 
54 
53 
52 
51 

43  40 
36 
32 
28 
24 

16  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.51  629 
9.51  666 
9.51  702 
9.  51  738 
9.51  774 

37 

36 
36 
36 
37 

9.54  106 
9.  54  147 
9.54  187 
9.  54  228 
9.  54  269 

41 

40 
41 
41 
40 

0.45  894 
0.  45  853 
0.  45  813 
0.  45  772 
0.  45  731 

9.  97  523 
9.  97  519 
9.  97  515 
9.  97  510 
9.97  506 

4 
4 
5 
4 
5 

50 

49 

48 
47 
46 

43  20 
16 
12 
8 
4 

17   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  51  811 
9.51  847 
9.  51  883 
9.51  919 
9.51  956 

36 
36 
36 
36 
36 

9.54  309 
9.54  350 
P.  54  390 
9.  54  431 
9.  54  471 

41 

40 
41 
40 
41 

0.  45  691 
0.45  650 
0.45  610 
0.45  569 
0.  45  529 

'  9.  97  501 
9.97  497 
9.  97  492 
9.  97  488 
9.  97  484 

4 
5 
4 
4 
5 

45 
44 
43 
42 
41 

43   0 

56 
52 
48 
44 

17  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.51  9C1 
9.  52  027 
9.  52  063 
9.  52  099 
9.  52  135 

36 
36 
36 
36 
36 

9.  54  512 
9.54  552 
9.  54  593 
9.  54  633 
9.  54  67? 

40 
41 
40 
40 
41 

0.  45  488 
0.  45  448 
0.  45  407 
0.  45  367 
0.  45  327 

9.  97  479 
9.  97  475 
9.  97  470 
9.  97  466 
9.  97  461 

4 
5 
4 
5 
4 

40 

39 
38 
37 
36 

42  40 
36 
32 

28 
24 

17  40 
44 
48 
52 
56 

26 

26 

27 
28 
29 

9.52  171 
9.  52  207 
9.  52  242 
9.  52  278 
9.  52  314 

36 
35 
36 
36 
36 

9.54  714 
9.54  754 
9.  54  794 
9.  54  835 
9.  54  875 

40 
40 
41 
40 
40 

0.  45  286 
0.  45  246 
0.  45  206 
0.45  165 

o.-ir,  I'jA 

9.  97  457 
9.  97  453 
9.  97  448 
9.  97  444 
9.  97  439 

4 
5 
4 
5 
4 

35 
34 
33 
32 
31 

42  20 

16 
12 
8 
4 

18   0 
4 

8 
12 
16 

30 

31 
32 
33 
34 

9.52  350 
9.52  385 
9.  52  421 
9.  52  456 
9.  52  492 

35 
36 
35 
36 
35 

9.  54  915 
9.54  95!? 
9.  54  995 
9.  55  0.35 
9.55  075 

40 
40 
40 
40 
40 

0.45  085 
0.  45  045 
0.  45  005 
0.  44  965 
0.44  925 

•  9.  97  435 
9.  97  430 
9.  97  426 
9.  97  421 
9.  97  417 

5 
4 
5 
4 
5 

30 

29 

28 
27 
26 

42   0 
56 
52 
48 
44 

18  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

(.l.  .V_>  r,-J7 
9.52  563 
9.52  598 
9.  52  634 
9.  52  669 

36 
35 
36 
35 
36 

9.55115 
9.55  155 
9.55  19^ 
9.  55  235 
9.  55  275 

40 
40 
40 
40 
40 

0.  ii  sxfi 
0.  44  845 
0.  44  805 
0.  44  765 
0.  44  725 

9.97  412 
9.97  408 
9.  97  403 
9.  97  399 
9.  97  394 

4 
5 
4 
5 
4 

25 
24 
23 
22 
21 

41  40 
36 

32 
28 
24 

18  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  52  705 
9.  52  74Q 
9.52  775 
9.  52  811 
9.  52  846 

35 
35 
36 
35 
35 

9.55  315 
9.  55  355 
9.  55  395 
9.55434 
9.  55  474 

40 
40 
39 
40 
40 

0.44  r,s.-> 
0.44  645 
0.  44  605 
0.  44  566 
0.  44  526 

9.97  390 
9.  97  385 
9.97  381 
9.  97  376 
9.  97  372 

5 
4 
5 
4 
5 

20 

19 
18 
17 
16 

41  20 
16 
12 

8 
1 

19   0 
4 

8 
12 
16 

45 

46 
47 
48 
49 

9.  52  881 
9.52  916 
9.  52  951 
9.  52  986 
9.53  021 

35 
35 
35 
35 
35 

9.55  514 
9.55554 
9.  55  593 
9.55  633 
9.55673 

40 
39 
40 
40 
39 

0.44  486 
0.  44  446 
0.  44  407 
0.44  367 
0.  44  327 

9.  97  367 
9.97  363 
9.  97  358 
9.  97  353 
9.  97  349 

4 

5 
5 
4 
5 

15 
14 
13 
12 
11 

41   0 

56 
52 
48 
44 

19  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  53  056 
9.53  092 
9.  53  126 
9.  53  161 
9.  53  196 

36 
34 
35 
35 
35 

9.55  712 
9.  55  752 
9.  55  791 
9.  55  831 
9.  55  870 

40 
39 
40 
39 
40 

0.44288 
0.  44  248 
0.44  209 
0.44  169 
0.  44  130 

9.  97  344 
9.  97  340 
9.  97  335 
9.  97  331 
9.  97  326 

4 
5 
4 
5 
4 

10 

9 

8 
7 
6 

40  40 
36 
32 

28 
24 

19  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

'.».  .",:;  -i:>,\ 
9.53  266 
9.53  301 
9.53  336 
9.  53  370 

36 
35 
35 
34 
35 

9.  55  910 
9.55949 
9.  55  989 
9.56  028 
9.56  067 

39 
40 
39 
39 
40 

0.44  090 
0.  44  051 
0.44  Oil 
0.43  972 
0.43  933 

9.  97  322 
9.  97  317 
9.  97  312 
9.  97  308 
9.  97  303 

5 
5 

4 
5 
4 

5 
4 
3 
2 
1 

40  20 
16 
12 

8 
4 

20   0 

60 

9.53  405 

9.56  107 

0.  43  893 

9.  97"299 

0 

40   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

70° 


168  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  20° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

20   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  53  405 
9.  53  440 
9.  53  475 
9.53  509 
9.53  544 

35 
35 
34 
35 
34 

35 
34 
35 
34 
35 

34 
34 
35 
34 
34 

35 
34 
34 
34 
34 

34 
34 
34 
34 
34 

34 
34 
34 
34 
34 

33 
34 
34 
33 
34 

34 
33 
34 
33 
34 

33 

34 
33 
34 
33 

33 
34 
33 
33 
33 

34 
33 
33 
33 
33 

33 
33 
33 
33 
33 

9.  56  107 
9.56  146 
9.56  185 
9.  56  224 
9.56  264 

39 
39 
39 
40 
39 

39 
39 
39 
39 
39 

39 
39 
39 
39 
39 

39 
39 
39 
39 
38 

39 
39 
39 
38 
39 

39 
38 
39 
38 
39 

38 
39 
38 
39 

38 

38 
39 
38 
38 
39 

38 
36 
38 
38 
39 

38 
38 
38 

38 
38 

38 
38 
38 
38 

38 

38 
37 
38 
38 
38 

0.  43  893 
0.  43  854 
0.  43  815 
0.  43  776 
0.  43  736 

9.  97  299 
9.  97  294 
9.  97  289 
9.  97  285 
9.  97  280 

5 
5 
4 
5 
4 

5 
5 

4 
5 

5 

4 
5 
5 
4 
5 

5 
4 
5 

5 
4 

5 
5 
4 
5 
5 

4 
5 
5 

5 
4 

5 
5 
4 
5 
5 

5 
4 
5 
5 
5 

4 
5 
5 
5 
5 

4 

5 
5 
5 
5 

4 
5 
5 
5 
5 

60 

59 
58 
57 
56 

40   0 

56 
52 
48 
44 

20  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  53  578 
9.53  613 
9.  53  647 
9.53  682 
9.  53  716 

9.  56  303 
9.  56  342 
9.  56  381 
9.  56  420 
9.56459 

0.43  697 
0.  43  658 
0.43  619 
0.43  580 
0.43  541 

9.  97  276 
9.97  271 
9.  97  266 
9.  97  262 
9.  97  257 

55 
54 
53 
52 
51 

39  40 
36 
32 
28 
24 

20  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.53  751 
9.  53  785 
9.  53  819 
9.  53  854 
9.53  888 

9.  56  498 
9.  56  537 
9.  56  576 
9.  56  615 
9.56  654 

0.43  502 
0.  43  463 
0.  43  424 
0.43  385 
0.  43  346 

9.  97  252 
9.  97  248 
9.  97  243 
9.  97  238 
9.  97  234 

60 

49 
48 
47 
46 

39  20 
16 
12 
8 
4 

21   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.53  922 
9.  53  957 
9.  53  991 
9.54  025 
9.54059 

9.56  693 
9.  56  732 
9.  56  771 
9.  56  810 
9.  56  849 

0.  43  307 
0.  43  268 
0.  43  229 
0.43  190 
0.43  151 

9.  97  229 
9.  97  224 
9.  97  220 
9.  97  215 
9.  97  210 

45 
44 
43 
42 
41 

39   0 
56 
52 
48 
44 

21  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.54  093 
9.  54  127 
9.  54  161 
9.  54  195 
9.  54  229 

9.  56  887 
9.56  926 
9.  56  965 
9.57  004 
9.57  042 

0.43  113 
0.  43  074 
0.  43  035 
0.42  996 
0.42  958 

9.  97  206 
9.  97  201 
9.  97  196 
9.97  192 
9.97  187 

40 

39 
38 
37 
36 

38  40 
36 
32 

28 
24 

21  40 
44 
48 
52 
56 

25 
26 

27 
28 
29 

9.  54  263 
9.54  297 
9.  54  331 
9.54  365 
9.  54  399 

9.57  081 
9.  57  120 
9.57  158 
9.  57  197 
9.57  22) 

0.42  919 
0.  42  880 
0.42  842 
0.  42  803 
0.42  765 

9.97  182 
9.97  178 
9.  97  173 
9.97  168 
9.97  163 

35 
34 
33 
32 
31 

38  20 
16 
12 

8 
4 

22   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  54  433 
9.  54  466 
9.54500 
9.  54  534 
9.  54  567 

«J.  57  274 
9.  57  312 
9.57  351 
9.  57  389 
9.57  428 

0.  42  726 
0.  42  688 
0.  42  649 
0.  42  611 
0.  42  572 

9.  97  159 
9.97  154 
9.  97  149 
9.97  145 
9.  97  140 

30 

29 
28 
27 
26 

38   0 
56 
52 

48 
44 

22  20 

24 
28 
32 
36 

35 
36 
•37 
38 
,39 

9.  54  601 
9.54  635 
9.  54  668 
9.  54  702 
9.  54  735 

9.  57  466 
9.  57  504 
9.  57  543 
9.  57  581 
9.  57  619 

0.  42  534 
0.  42  496 
0.  42  457 
0.42  419 
0.  42  381 

9.  97  135 
9.97  130 
9.97  126 
9.  97  121 
9.  97  116 

25 
24 
23 
22 
21 

37  40 
36 
32 
28 
24 

22  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  54  769 
9.54  802 
9.  54  836 
9.  54  869 
9.54  903 

9.  57  658 
9.  57  696 
9.  57  734 
9.57  772 
9.  57  810 

0.  42  342 
0.  42  304 
0.  42  266 
0.  42  228 
0.  42  190 

9.97  111 
9.  97  107 
9.97  102 
9.  97  097 
9.97  092 

20 

19 
18 
17 
16 

37  20 
16 
12 

8 
4 

23   0 

4 
8 
12 
16 

45 

46 
47 
48 
49 

9.  54  936 
9.  54  969 
9.  55  003 
9.55  036 
9.55069 

9.  57  849 
9.  57  887 
9.  57  925 
9.  57  963 
9.58  001 

0.  42  151 
0.42  113 
0.42  075 
0.  42  037 
0.41  999 

9.  97  087 
9.  97  083 
9.  97  078 
9.  97  073 
9.97  068 

15 

14 
13 
12 
11 

37   0 
56 
52 
48 
44 

23  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  55  102 
9.  55  136 
9.  55  169 
9.  55  202 
9.  55  235 

9.58  039 
9.58  077 
9.  58  115 
9.58  153 
9.58  191 

0.  41  961 
0.  41  923 
0.41  885 
0.41  847 
0.41  809 

9.  97  063 
9.  97  059 
9.  97  054 
9.  97  049 
9.97  044 

10 

9 

8 
7 
6 

36  40 
36 
32 
28 
24 

23  40 

44 
48 
52 
56 

65 
56 
57 

58 
59 

9.  55  268 
9.  55  301 
9.  55  334 
9.  55  367 
9.55400 

9.  58  229 
9.  58  267 
9.  58  304 
9.  58  342 
9.58380 

0.41  771 
0.41  733 
0.41  696 
0.  41  658 
0.  41  620 

9.  97  039 
9.  97  035 
9.  97  030 
9.  97  025 
9.  97  020 

4 
5 
5 
5 
*, 

5 
4 
3 
2 

1 

86  20 
16 
12 
8 
4 

24   0 

60 

9.  55  433 

9.  58  418 

0.41  582 

9.  97  015 

0 

36   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s 

69° 


GEOGRAPHIC   TABLES    AND    FORMULAS.  169 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  21° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

24   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.55  433 
9.55  466 
9.55499 
9.55  532 
9.55  564 

33 
33 
33 
32 
33 

33 
33 
32 
33 
33 

9.58  418 
9.58  455 
9.58  493 
9.  58  531 
9.58  569 

37 
38 
38 
38 
37 

38 
37 
38 
38 
37 

38 
37 
38 
37 
37 

38 
37 
38 
37 
37 

37 
38 
37 
37 
37 

37 
38 
37 
37 
37 

37 
37 
37 
37 

37 

37 
37 
36 
37 
37 

37 
37 
36 
37 
37 

37 
36 
37 
37 
36 

37 
36 
37 
36 
37 

36 
37 
36 
37 
36 

0.41  582 
0.41  545 
0.  41  507 
0.41  469 
0.41  431 

9.  97  015 
9.  97  010 
9.97  005 
9.  97  001 
9.  96  996 

5 
5 
4 
5 
5 

5 
5 
5 
5 
5 

4 
5 
5 
5 
5 

5 
5 
5 
5 
5 

5 
5 

4 
5 
5 

5 
5 
5 
5 
5 

5 
5 
5 
5 
5 

5 
5 
5 
5 
5 

5 
5 
5 
5 
5 

5 
5 
5 
6 
5 

5 
5 

5 
5 
5 

60 

59 
58 
57 
56 

36   0 
56 
52 
48 
44 

24  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.55  597 
9.55  630 
9.55  663 
9.55  695 
9.  55  728 

9.58  606 
9.  58  644 
9.  58  681 
9.  58  719 
9.  58  757 

0.41  394 
0.41  356 
0.  41  319 
0.  41  281 
0.41  213 

9.  96  991 
9.  96  986 
9.  96  981 
9.  96  976 
9.96  971 

55 
54 
53 
52 
51 

35  40 
36 
32 

28 
24 

24  40 
44 
48 
52 
56 

10 

11 
12 
13 

14 

9.  55  761 
9.  55  793 
9.  55  826 
9.55  858 
9.  55  891 

32 
33 
32 
33 
32 

33 
32 
33 
32 
32 

33 
32 
32 
33 
32 

32 
32 
32 
32 
33 

32 
32 
32 
32 
32 

31 

32 
32 
32 
32 

32 
31 
32 
32 
32 

31 

32 
31 
32 
32 

31 
32 
31 
31 
32 

31 
32 
31 
31 
32 

9.  58  794 
9.  58  832 
9.58  869 
9.58  907 
9.58  944 

0.  41  206 
0.41  168 
0.41  131 
0.41  093 
0.41  056 

9.96  966 
9.  96  962 
9.  96  957 
9.96  952 

9.  96  947 

50 

49 
48 
47 
46 

35  20 
16 

12 
8 
4 

25   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.55  923 
9.65  956 
9.55  988 
9.  56  021 
9.56053 

9.58  981 
9.  59  019 
9.59  066 
9.  59  094 
9.59  131 

0.41  019 
0.  40  981 
0.40  944 
0.40  906 
0.40  869 

9.  96  942 
9.  96  937 
9.  96  932 
9.  96  927 
9.%  922 

45 
44 
43 
42 
41 

35   0 
56 
52 
48 
44 

25  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.56  085 
9.56  118 
9.56  150 
9.  56  182 
9.  56  215 

9.  59  168 
9.59205 
9.  59  243 
9.59  280 
9.  59  317 

0.  40  832 
0.  40  795 
0.40  757 
0.40  720 
0.40  683 

9.  96  917 
9.  96  912 
9.%  907 
9.%  903 
9.  96  898 

40 

39 
38 
37 
36 

34  40 
36 
32 
28 
24 

25  40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.  56  247 
9.  56  279 
9.  56  311 
9.56  343 
9.  56  375 

9.59  354 
9.59  391 
9.59  429 
9.  59  466 

y.5y  ."><»:; 

0.  40  646 
0.40609 
0.  40  571 
0.40534 
0.  40  497 

9.96  893 
9.%  888 
9.  96  883 
9.  96  878 
9.96  873 

35 
34 
33 
32 
31 

34  20 
16 
12 
8 
4 

26   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.56  408 
9.56  440 
9.56  472 
9.56  504 
9.56  536 

9.59  540 
9.  59  577 
9.  59  614 
9.  59  651 

y.  59  osx 

0.  40  460 
0.  40  423 
0.40  386 
0.40  349 
0.40  312 

9.96  868 
9.96  863 
9.96  858 
9.%  853 
9.  96  848 

30 

29 
28 
27 
26 

34   0 
56 
52 
48 
44 

26  20 
24 
28 
32 
36 

35 

36 
37 
38 
39 

9.56  568 
9.56  599 
9.  56  631 
9.56  663 
9.56  695 

9.59  725 
9.  59  762 
9,59  799 
9.59  835 
9.  59  872 

0.  40  275 
0.  40  238 
0.40  201 
0.  40  165 
0.  40  128 

9.96  843 
9.  96  838 
9.  96  833 
9.  96  828 
9.  96  823 

25 
24 
23 
22 
21 

33  40 
36 
32 

28 
24 

26  40 
44 
48 
52 
56 

40 

41 
42 
43 

44 

9.56  727 
9.56  759 
9.  56  790 
9.  56  822 
9.56  854 

9.59  909 
9.  59  946 
9.  59  983 
9.  60  019 
9.60  056 

0.40  091 
0.  40  051 
0.  40  017 
0.  39  981 
0.  39  944 

9.  %  818 
9.  96  813 
9.  96  808 
9.96  803 
9.96  798 

20 

19 
18 
17 
16 

33  20 
16 
12 

8 
4 

27   0 
4 
8 
12 
16 

45 
46 

47 
48 
49 

9.56  886 
9.56  917 
9.56  949 
9.56  980 
9.  57  012 

9.60  093 
9.60  130 
9.60  166 
9.  60  203 
9.  60  240 

0.  39  907 
0.  39  870 
0.  39  834 
0.  39  797 
0.  39  760 

9.  96  793 
9.96  788 
9.  96  783 
9.  96  778 
9.  96  772 

15 
14 
13 
12 
11 

33   0 
56 
52 
48 
44 

27  20 
24 
28 
32 
36 

50 

51 
52 
53 

54 

9.57  044 
9.  57  075 
9.57  107 
9.57  138 
9.  57  169 

9.  60  276 
9.  60  313 
9.60  349 
9.60  386 
9.  60  422 

0.39  724 
0.  39  687 
0.  39  65-1 
0.  39  614 
0.  39  578 

9.  96  767 
9.  96  762 
9.  96  757 
9.96  752 
9.96  747 

10 

9 
8 
7 
6 

32  40 
36 
32 
28 
24 

27  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  57  201 
9.  57  232 
9.57  264 
9.57  295 
9.  57  326 

9.  60  459 
9.  60  495 
9.  60  532 
9.60  568 
9.60  605 

0.  39  541 
0.39  505 
0.  39  468 
0.  39  432 
0.39395 

9.96  742 
9.  96  737 
9.  96  732 
9.  96  727 
9.  96  722 

5 
5 
5 
5 
5 

5 
4 
3 
2 
1 

32  20 
16 
12 
8 
4 

28   0 

60 

9.57  358 

9.60  641 

0.  39  359 

9.96  717 

0 

32   0 

I*  Los. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

68° 


170  GEOGEAPHIC   TABLES    AND   FORMULAS. 

TARLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
lh  22° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

28   0 
4 
8 
12 
16 

0 

] 
2 
3 
4 

9.  57  358 
9.  57  389 
9.  57  420 
9.  57  451 
9.  57  482 

31 

31 
31 
31 
32 

9.  60  641 
9.  60  677 
9.  60  714 
9.  60  750 
9.  60  786 

36 
37 
36 
36 
37 

0.39  359 
0.  39  323 
0.  39  286 
0.39  250 
0.  39  214 

9.  96  717 
9.  96  711 
9.  96  706 
9.  96  701 
9.  96  696 

6 
5 
5 
5 
5 

60 

59 

58 
57 
56 

32   0 
56 
52 
48 
44 

28  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  57  514 
9.57  545 
9.  57  576 
9.57  607 
9.  57  638 

31 
31 
31 
31 
31 

9.  60  823 
9.  60  859 
9.  60  895 
9.  60  931 
9.  60  967 

36 
36 
36 
36 
37 

0.  39  177 
0.  39  141 
0.  39  105 
0.  39  069 
0.  39  033 

9.  96  691 
9.  96  686 
9.  96  681 
9.  96  676 
9.  96  670 

5 
5 
5 
6 
5 

55 
54 
53 
52 
51 

31  40 
36 
32 
28 
24 

28  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.57  669 
9.57  700 
9.57  731 
9.  57  762 
9.  57  793 

31 
31 
31 
31 
31 

9.61  004 
9.  61  040 
9.  61  076 
9.61  112 
9.61  148 

36 
36 
36 
86 
36 

0.  38  996 
0.  38  960 
0.38  924 
0.  38  888 
0.  38  852 

9.  96  665 
9.  96  660 
9.  96  655 
9.  96  650 
9.96  645 

5 
5 
5 
5 
5 

50 

49 
48 
47 
46 

31  20 

16 
12 
8 
4 

29   0 

4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  57  824 
9.57  855 
9.57  885 
9.  57  916 
9.  57  947 

31 

30 
31 
31 
31 

9.61  184 
9.61  220 
9.  61  256 
9.61  292 
9.61  328 

36 
36 
36 
36 
36 

0.  38  816 
0.38  780 
0.  38  744 
0.  38  708 
0.  38  672 

9.96  640 
9.  96  634 
9.  96  629 
9.  96  624 
9.  96  619 

6 

5 
5 
5 
5 

45 
44 
43 
42 
41 

31   0 
56 
52 
48 
44 

29  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  57  978 
9.58  008 
9.  58  039 
9.  58  070 
9.58  101 

30 
31 
31 
31 
30 

9.61  364 
9.61  400 
9.  HI  436 
9.61  472 
9.  61  508 

36 
36 
36 
36 
36 

0.38  636 
0.  38  600 
0.  38  564 
0.  38  528 
0.  38  492 

9.  96  614 
9.  96  608 
9.  96  603 
9.  96  598 
9.  96  593 

6 
5 
5 
5 
5 

40 

39 
38 
37 
36 

30  40 
36 
32 
28 
24 

29  40 
44 

48 
52 
56 

25 
26 
27 
28 
29 

9.  58  131 
9.  58  162 
9.  58  192 
9.58  223 
9.  58  253 

31 

30 
31 
30 
31 

9,61  544 
9.61  579 
9.  61  615 
9.61  651 
9.61  687 

35 
36 
36 
36 
35 

0.  38  456 
0.  38  421 
0.  38  385 
0.  38  349 
0.  38  313 

9.  96  588 
9.  96  582 
9.  96  577 
9.96  572 
9.  96  567 

6 
5 
5 
5 
5 

35 
34 
33 
32 
31 

30  20 
16 
12 
8 
4 

30   0 

4 
8 
12 
16 

30 

31 
32 
33 
34 

9.58  284 
9.58  314 
9.  58  345 
9.  58  375 
9.  58  406 

30 
31 
30 
31 
30 

9.61  722 
9.61  758 
9.61  794 
9.61  830 
9.  61  865 

36 
36 
.36 
35 
36 

0.  38  278 
0.  38  242 
0.  38  206 
0.  38  170 
0.38  135 

9.  96  562 
9.96  556 
9.96  551 
9.  96  546 
9.96  541 

6 
5 
5 
5 
6 

30 

29 

28 
27 
26 

30   0 
56 
52 
48 
44 

30  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.58  436 
9.  58  467 
9.  58  497 
9.  58  527 
9.58  557 

31 
30 
30 
30 
31 

9.61  901 
9.61  936 
9.61  972 
9.  62  008 
9.  62  043 

35 
36 
36 
35 
36 

0.  38  099 
0.  38  064 
0.  38  028 
0.37  992 
0.  37  957 

9.  96  535 
9.  96  530 
9.  96  525 
9.  96  520 
9.96  514 

5 
5 
5 
6 
5 

25 
24 
23 
22 
21 

29  40 
36 
32 
28 
24 

30  40 

44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  58  588 
9.  58  618 
9.  58  648 
9.  58  678 
9.  58  709 

30 
30 
30 
31 
30 

9.  62  079 
9.  62  114 
9.62  150 
9.62  185 
9.  62  221 

35 
36 
35 
36 
35 

0.37  921 
0.  37  886 
0.  37  850 
0.  37  815 
0.  37  779 

9.  96  509 
9.  96  504 
9.  96  498 
9.  96  493 
9.  96  488 

5 
6 
5 
5 
5 

20 

19 

18 
17 
16 

29  20 
16 
12 
8 
4 

31   0 

4 
8 
12 
16 

45 
46 
47 
48 
49 

9.  58  739 
9.  58  769 
9.  58  799 
9.  58  829 
9.  58  859 

30 
30 
30 
30 
30 

9,  62  256 
9.  62  292 
9.  62  327 
9.  62  362 
9.  62  398 

36 
35 
25 
36 
35 

0.37  744 
0.  37  708 
0.  37  673 
0.37  638 
0.37  602 

9.  96  483 
9.  96  477 
9.  96  472 
9.  96  467 
9.96  461 

6 
5 
5 
6 
5 

15 
14 
13 
12 
11 

29   0 
56 
52 
48 
44 

31  20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.  58  889 
9.58  919 
9.58  949 
9.  58  979 
9.  59  009 

30 
30 
30 
30 
30 

9.  62  433 
9.  62  468 
9.62  504 
9.  62  539 
9.  62  574 

35 
36 
35 
35 
35 

0.  37  567 
0.  37  532 
0.37  49n 
0.  37  461 
0.  37  426 

9.  96  456 
9.  96  451 
9.  96  445 
9.  96  440 
9.  96  4&5 

5 
6 
5 
5 
6 

10 

9 

8 

6 

28  40 
36 
32 
28 
24 

31  40 

44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  59  039 
9.  59  069 
9.  59  098 
9.  59  128 
9.59  158 

30 
29 
30 
30 
30 

9.  62  609 
9.  62  645 
9.  62  680 
9.  62  715 
9.  62  750 

36 
'  35 
35 
35 
35 

0.  37  391 
0.37  355 
0.37  320 
0.  37  285 
0.  37  250 

9.  96  429 
9.  96  424 
9.  96  419 
9.  96  413 
9.  96  408 

5 
5 
6 
5 
5 

5 
4 
3 
2 
1 

28  20 
16 
12 
8 
4 

32   0 

60 

9.  59  188 

9.  62  785 

0.  37  215 

9.  96  403 

0 

28   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

i 

m.  s. 

67° 


GEOQKAPHIC   TABLES    AND    FORMULAS.  171 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh        *  23° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

32   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.59  188 
9.  59  218 
9.  59  247 
9.  59  277 
9.  59  307 

30 
29 
30 
30 

29 

9.  62  785 
9.  62  820 
9.  62  855 
9.  62  890 
9.62  926 

35 
35 
35 
36 
35 

0.37215 
0.37  180 
0.37  145 
0.  37  110 
0.  37  074 

9.  96  403 
9.  96  397 
9.  96  392 
9.  96  387 
9.96  381 

6 
5 
5 
6 

<> 

60 

59 

58 
57 
56 

28   0 
56 
52 
48 
44 

32   20 
24 

28 
32 
36 

5 
6 
7 
8 
9 

9.  59  336 
9.59  366 
9.  59  396 
9.59  425 
9.  59  455 

30 
30 
29 
30 
29 

9.  62  961 
9.62  996 
9.  63  031 
9.63  066 
9.63  101 

35 
35 
35 
35 
34 

0.  37  039 
0.  37  004 
0.  36  969 
0.  36  934 
0.  36  899 

9.  96  376 
9.  96  370 
9.96  365 
9.96  360 
9.96  354 

6 
5 

5 
6 

5 

55 
54 
53 
52 
51 

27   40 

36 
32 

28 
24 

32   40 
44 

48 
52 
56 

10 

11 
12 

13 
14 

9.59  484 
9.  59  514 
9.  59  543 
9.  59  573 
9.59  602 

30 
29 
30 
29 
30 

9.  63  135 
9.63  170 
9.63  205 
9.  63  240 
9.  63  275 

35 
35 
35 
35 
35 

0.36  865 
0.  36  830 
0.36  795 
0.36  760 
0.  36  725 

9.  96  349 
9.96  343 
9.96  338 
9.  96  333 
9.  96  327 

6 
5 
5 
6 
5 

50 

49 
48 
47 
46 

27   20 
16 
12 

8 
4 

33   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  59  632 
9.  59  661 
9.  69  690 
9.  59  720 
9.59  749 

29 
29 
30 
29 
29 

9.  63  310 
9.63  345 
9.  63  379 
9.63414 
9.63  449 

35 
34 
35 
35 
35 

0.  36  690 
0.  36  655 
0.  36  621 
0.36  586 
0.  36  551 

9.96  322 
9.  96  316 
9.  96  311 
9.  96  305 
9.96  300 

6 
5 
6 
5 
6 

45 
44 
43 
42 
41 

27   0 
56 
52 
48 
44 

33   20 
24 
28 
32 
36 

20 

21 

22 
23 
24 

9.59  778 
9.  59  808 
9.59837 
9.  59  866 
9.  59  895 

30 
29 
29 
29 
29 

9.63  484 
9.  63  519 
9.63  553 
9.63  588 
9.63  623 

35 
34 
35 
35 
34 

0.  36  516 
0.  36  481 
0.  36  447 
0.  36  412 
0.  36  377 

9.96  294 
9.  96  289 
9.96  284 
9.  96  278 
9.96273 

5 
5 
6 
5 
6 

40 

39 
38 
37 
36 

26   40 
36 
32 
28 
24 

33   40 
44 
48 
52 
56 

•jr. 
26 
27 
28 
29 

9.59  924 
9.  59  954 
9.59  983 
9.  60  012 
9.60  041 

30 

29 
29 
29 
29 

9.63  657 
9.63  692 
9.63  726 
9.  63  761 
9.63  796 

35 
34 
35 
35 
34 

0.36  343 
0.36  308 
0.  36  274 
0.  36  239 
0.  36  204 

9.  96  267 
9.  96  262 
9.  96  256 
9.  96  251 
9.  96  245 

5 
6 
5 
6 
5 

35 
34 
33 
32 
31 

26   20 
16 
12 

8 
4 

34   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  60  070 
9.60  099 
9.60  128 
9.  60  157 
9.60  186 

29 
29 
29 
29 
29 

9.63  830 
9.63  865 
9.63  899 
9.63  934 
9.63968 

35 
34 
35 
34 
35 

0.36  170 
0.36  135 
0.36  101 
0.36  066 
0.  36  032 

9.96  240 
9.96  234 
9.  96  229 
9.  96  223 
9.  %  218 

6 
5 
6 
5 
6 

30 

29 
28 
27 
26 

26   0 

56 
52 
48 
44 

34   20 
24 
28 
32 
36 

35 
36 
37 

38 

39 

9.  60  215 
9.  60  244 
9.60  273 
9.60  302 
9.60  331 

29 
29 
29 
29 
28 

y.  M  OOH 

9.  64  037 
9.64  072 
9.64  106 
9.64  140 

34 
35 
34 
34 
35 

0.35  997 
0.35  963 
0.35  928 
0.  35  894 
0.  35  860 

9.  96  212 
9.  96  207 
9.  96  201 
9.  96  196 
9.96  190 

5 
6 
5 
6 
5 

25 
24 
23 
22 
21 

25   40 
36 
32 

28 
24 

34   40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.60359 
9.60  388 
9.  60  417 
9.  60  446 
9.  60  474 

29 
29 
29 
28 
29 

9.64  175 
9.64  209 
9.  64  243 
9.  64  278 
9.  64  312 

34 
34 
35 
34 

34 

0.35825 
0.  35  791 
0.  35  757 
0.  35  722 
0.35  688 

9.  96  185 
9.96  179 
9.96  174 
9.  96  168 
9.  96  162 

6 
5 
6 
6 
5 

20 

19 
18 
17 
16 

25   20 
16 
12 

8 
4 

35   0 

4 
8 
12 
16 

45 
46 

47 
48 
49 

9.60  503 
9.  60  532 
9.60  561 
9.  60  589 
9.  60  618 

29 
29 
28 
29 
28 

9.64  346 
9.64  381 
9.  64  415 
9.  64  449 
9.64  483 

35 
34 
34 
34 
34 

0.35  654 
0.  35  619 
0.35  585 
0.35  551 
0.  35  517 

9.96  157 
9.  96  151 
9.96  146 
9.  96  140 
9.  96  135 

6 
5 
6 
5 
6 

15 
14 
13 
12 
11 

25   0 

56 
52 
48 
44 

35   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  60  646 
9.  60  675 
9.  60  704 
9.  60  732 
9.  60  761 

29 
29 

28 
29 

28 

9.  64  517 
9.  64  552 
9.64  586 
9.64  620 
9.64  654 

35 
34 
34 
34 
34 

0.35  483 
0.  35  448 
0.35414 
0.35  380 
0.35  346 

9.  96  129 
9.96  123 
9.  96  118 
9.96  112 
9.96  107 

6 
5 
6 
5 
6 

10 

9 

8 
7 
6 

24   40 
36 
32 
28 
24 

35   40 
44 

48 
62 
56 

55 
56 

57 
58 
59 

9.  60  789 
9.60  818 
9.60  846 
9.60  875 
9.60  903 

29 
28 
29 
28 
28 

9.64  688 
9.64  722 
9.64  756 
9.64  790 
9.64  824 

34 
34 
34 
34 
34 

0.  35  212 
0.35  278 
0.35  244 
0.35  210 
0.  35  176 

9.  96  101 
9.  96  095 
9.  96  090 
9.  96  084 
9.96  079 

6 
5 
6 
5 
6 

5 
4 
3 
2 

1 

24   20 
16 
12 
8 
4 

36   0 

60 

9.  60  931 

9.64  858 

0.35  142 

9.96  073 

0 

24   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 
I 

172  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
lh  24° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

36   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  60  931 
9.  60  960 
9.60  988 
9.61  016 
9.61  045 

29 
28 
28 
29 

9.  64  858 
9.64  892 
9.64  926 
9.  64  960 
9.64994 

34 
34 
34 
34 

0.  35  142 
0.  35  108 
0.  35  074 
0.35  040 
0.35  006 

9.  96  073 
9.  96  067 
9.  96  062 
9.  96  056 
9.  96  050 

6 
5 
6 
6 

60 

69 
58 
57 
56 

24   0 
56 
52 
48 
44 

36  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  61  073 
9.61  101 
9.61  129 
9.  61  158 
9.  61  186 

28 
28 
29 
28 

9.65  028 
9.  65  062 
9.  65  096 
9.  65  130 
9.65  164 

34 
34 
34 
34 

0.34  972 
0.  34  938 
'0.  34  904 
0.  34  870 
0.  34  836 

9.  96  045 
9.96  039 
9.  96  034 
9.  96  028 
9.96  022 

6 
5 
6 
6 

55 
54 
53 
52 
51 

23  iO 
36 
32 
28 
24 

36  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  61  214 
9.61  242 
9.61  270 
9.  61  298 
9.61  326 

28 
28 
28 
28 

9.  65  197 
9.65  231 
9.  65  265 
9.  65  299 
9.65  333 

34 
34 
34 
34 

0.  34  803 
0.  34  769 
0.34  735 
0.  34  701 
0.34  667 

9.  96  017 
9.  96  Oil 
9.  96  005 
9.96  000 
9.  95  994 

6 
6 
5 
6 

50 

49 
48 
47 
46 

23  20 
16 
12 
8 
4 

37   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.61  354 
9.  61  382 
9.  61  411 
9.  61  438 
9.  61  466 

28 
29 
27 

28 

9.  65  366 
9.  «5  400 
9.  65  434 
9.  65  467 
9.  65  501 

34 
34 
33 
34 

0.34634 
0.34  600 
0.34  566 
0.  34  533 
0.  34  499 

9.  95  988 
9.  95  982 
9,  95  977 
9.95  971 
9.  95  965 

6 
5 
6 
6 

45 
44 
43 
42 
41 

23   0 

56 
52 
48 
44 

37  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  61  494 
9.61  522 
9.61  550 
9.61  578 
9.  61  606 

28 

28 
28 
28 

9.  65  535 
9.  65  568 
9.  65  602 
9.  65  636 
9.  65  669 

33 
34 
34 
33 

0.  34  465 
0.  34  432 
0.  34  398 
0.  34  364 
0.  34  331 

9.95  960 
9.  95  954 
9.  95  948 
9.  95  942 
9.  95  937 

6 
6 
6 
5 

40 

39 
38 
37 
36 

22  40 
36 
32 
28 
24 

37  40 
44 

48 
52 
56 

25 
26 
27 
28 
29 

9.  61  634 
9.  61  662 
9.61  689 
9.  61  717 
9.61  745 

,  28 
27 

28 
28 

9.  65  703 
9.65  736 
9.  65  770 
9.  65  803 
9.  65  837 

33 
34 
33 
34 

0.  34  297 
0.  34  264 
0.  34  230 
0.  34  197 
0.  34  163 

9.  95  931 
9.95  925 
9.  95  920 
9.  95  914 
9.95  908 

6 
5 
6 
6 

35 
34 
33 
32 
31 

22  20 
16 
12 

8 
4 

38   0 

4 
8 
12 
16 

30 

31 
32 

34 

9.  61  773 
9.  61  800 
9.61  828 
9.61  856 
9.61  883 

27 
28 
28 
27 

9.  65  870 
9.65  904 
9.  65  937 
9.65  971 
9.66  004 

34 
33 
34 
33 
04 

0.  34  130 
0.  34  096 
0.  34  063 
0.  34  029 
0.33  996 

9.95  902 
9.  95  897 
9.  95  891 
9.95  885 
9.  95  879 

5 
6 
6 
6 

30 

29 
28 
27 
26 

2-2   0 
56 
52 
48 
44 

38  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.61  911 
9.61  939 
9.61  966 
9.61  994 
9.  62  021 

28 
27 
28 
27 

9.  66  038 
9.  66  071 
9.66  104 
9.  66  138 
9.66  171 

33 
33 
34 
33 

.0.33  962 
0.  33  929 
0.  33  896 
0.  33  862 
0.33  829 

9.  95  873 
9.  95  868 
9.  95  862 
9.95  856 
9.95  850 

5 
6 
6 
6 

25 
24 
23 

22 
21 

21  40 
36 
32 
28 
24 

38  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  62  049 
9.  62  076 
9.  62  104 
9.  62  131 
9.62  159 

27 

28 
27 
28 

9.  66  204 
9.  66  238 
9.66  271 
9.66  304 
9.  66  337 

34 
33 
33 
33 

0.  33  796 
0.  33  762 
0.33  729 
0.  33  696 
0.33  663 

9.95  844 
9.  95  839 
9.  95  833 
9.  95  827 
9.  95  821 

5 
6 
6 
6 

20 

19 

18 
17 
16 

21  20 
16 
12 
8 
4 

39   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.62  186 
9.  62  214 
9.  62  241 
9.  62  268 
9.  62  296 

28 
27 
27 
28 

9.  66  371 
9.  66  404 
9.  66  437 
9.  66  470 
9.66  503 

33 
33 
33 
33 
04 

0.  33  629 
0.  33  596 
0.  33  563 
0.  33  530 
0.  33  497 

9.  95  815 
9.  95  810 
9.  95  804 
9.  95  798 
9.95  792 

5 
6 
6 
6 

15 
14 
13 
12 
11 

21   0 
56 
52 
48 
44 

39  20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.  62  323 
9.62  350 
9.  62  377 
9.  62  405 
9.  62  432 

27 

27 
28 
27 

9.  66  537 
9.66  570 
9.  66  603 
9.66  636 
9.66  669 

33 
33 
33 
33 

0.33  463 
0.33  430 
0.  33  397 
0.33  364 
0.33  331 

9.  95  786 
9.  95  780 
9.95  775 
9.95  769 
9.  95  763 

6 
5 
6 
6 

10 

9 

8 
7 
6 

20  40 
36 
32 
28 
24 

39  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.  62  459 
9.  62  486 
9.  62  513 
9.62  541 
9.62  568 

27 

27 
28 
27 

9.66  702 
9.  66  735 
9.66  768 
9.66  801 
9.66  834 

33 
33 
33 
33 

0.  33  298 
0.  33  265 
0.  33  232 
0.33  199 
0.33  166 

9.95  757 
9.  95  751 
9.  95  745 
9.95  739 
9.95  733 

6 
6 
6 
6 

5 
4 
3 
2 
1 

20  20 
16 
12 
8 
4 

40   0 

60 

9.  62  595 

9.  66  867 

0.  33  133 

9.  95  728 

0 

20   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

65( 


GEOGRAPHIC  TABLES  AND  FORMULAS.  173 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  25° 


m.  s. 

> 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

40   0 
4 
8 
12 
16 

0 

1 

2 
3 
4 

9.  62  595 
9.  62  622 
9.  62  649 
9.62  676 
9.  62  703 

27 
27 
27 
27 

9.66  867 
9.66  900 
9.  66  9a3 
9.  66  966 
9.66  999 

33 
33 
33 
33 

0.33  133 
0.33  100 
0.  33  067 
0.  33  034 
0.  33  001 

9.  95  728 
9.  95  722 
9.  95  716 
9.  95  -710 
9.  95  704 

6 
6 
6 
6 

60 

59 
58 
57 
56 

20   0 
56 
52 
48 
44 

40  20 
24 
28 
32 
36 

5 

6 

8 
9 

9.  62  730 
9.62  757 
9.  62  784 
9.  62  811 
9.62  838 

27 
27 
27 
27 

9.  67  032 
9.67  065 
9.67  098 
9.67  131 
9.67  163 

33 
33 
33 
32 

0.  32  968 
0.  32  935 
0.  32  902 
0.  32  869 
0.  32  837 

9.95698 
9.95  692 
9.  95  686 
9.  95  680 
9.  95  674 

6 
6 
6 
6 

55 
54 
53 
52 
51 

19  40 
36 
32 
28 
24 

40  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  62  865 
9.  62  892 
9.  62  918 
9.62  945 
9.  62  972 

27 
26 
27 
27 

9.67  196 
9.  67  229 
9.  67  262 
9.  67  295 
9.  67  327 

33 
33 
33 
32 

0.32  804 
0.  32  771 
0.  32  738 
0.  32  705 
0.  32  673 

9.95  668 
9.  95  663 
9.  95  657 
9.95651 
9.  95  645 

5 
6 
6 
6 

50 

49 
48 
47 
46 

19  20 
16 
12 

8 
4 

41   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.62  999 
9.63  026 
9.63  052 
9.63  079 
9.63  106 

27 
26 
27 
27 

9.  67  360 
9.  67  393 
9.  67  426 
9.  67  458 
9.67  491 

33 
33 
32 
33 

0.  32  640 
0.32  607 
0.  32  574 
0.  32  5-12 
0.32509 

9.  95  639 
9.  95  633 
9.  95  627 
9.  95  621 
9.95615 

6 
6 
6 
6 

45 
44 
43 
42 
41 

19   0 
56 
52 

48 
44 

41  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  63  133 
9.  63  159 
9.63  186 
9.63213 
9.  63  239 

26 

27 
27 
26 

9.  67  524 
9.67  556 
9.  67  589 
9.  67  622 
9.67  654 

32 
33 
33 
32 

0.  32  476 
0.32  444 
0.  32  411 
0.  32  378 
0.  32  346 

9.95609 
9.  95  603 
9.  95  597 
9.  95  591 
9.95  585 

6 
6 
6 
6 

40 

39 
38 
37 
36 

18  40 
36 
32 
28 
24 

41  40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

9.63  266 
9.  63  292 
9.  63  319 
9.63  345 
9.  63  372 

26 
27 
26 
27 

9.  67  687 
9.  67  719 
9.67  752 
9.67  785 
9.67  817 

32 
33 
33 
32 

0.32  313 
0.  32  281 
0.  32  248 
0.  32  215 
0.  32  183 

9.  95  579 
9.  95  673 
9.  95  567 
9.  95  5-51 
9.95  555 

6 
6 
6 
6 

35 
34 
33 
32 
31 

18  20 
16 
12 
8 
4 

42   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  63  398 
9.63  425 
9.  63  451 
9.  63  478 
9.63  504 

27 
26 
27 
26 

9.67  850 
9.  67  882 
9.  67  915 
9.  67  947 
9.  67  980 

32 
33 
32 
33 

0.32  150 
0.32  118 
0.32  085 
0.32053 
0.  32  020 

9.  95  549 
9.  95  543 
9.  95  537 
9.  95  531 
9.95  525 

6 
6 
6 
6 

30 

29 

28 
27 
26 

18   0 
56 
52 
48 
44 

42  20 
24 
28 
32 
36 

36 
36 
37 
38 
39 

9.63531 
9.  63  557 
9.63  583 
9.  63  610 
9.63  636 

26 
26 
27 
26 

9.68012 
9.68  044 
9.  68  077 
9.68  109 
9.  68  142 

32 
33 
32 
33 

0.31  988 
0.31  956 
0.31  923 
0.31  891 
0.31  858 

9.  95  519 
9.95  513 
9.  95  507 
9.95500 
9.  95  494 

6 
6 

'  7 
6 

25 
24 
23 
22 
21 

17  40 
36 
32 
28 
24 

42  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.63  662 
9.63  689 
9.  63  715 
9.  63  741 
9.  63  767 

27 
26 
26 
26 

9.  68  174 
9.  68  206 
9.  68  239 
9.  68  271 
9.68  303 

32 
33 
32 
32 

0.31  826 
0.31  794 
0.31  761 
0.  31  729 
0.  31  697 

9.  95  488 
9.  95  482 
9.  95  476 
9.  95  470 
9.95464 

6 
6 
6 
6 

20 

19 
18 
17 
16 

17  20 
16 
12 
8 
4 

43   0 
4 

8 
12 
16 

45 
46 
47 
48 
49 

9.63  794 
9.  63  820 
9.63  846 
9.  63  872 
9.63  898 

26 
26 
26 
26 

9.  fi«  336 
9.68  368 
9.  68  400 
9.  68  432 
9.68  465 

33 

32 
32 
32 
33 

0.  31  664 
0.31  632 
0.31  600 
0.  31  568 
0.  31  535 

9.  95  458 
9.  95  452 
9.  95  446 
9.  95  440 
9.  95  434 

6 
6 
6 
6 

15 
14 
13 
12 
11 

17   0 
56 
52 
48 
44 

43  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.63  924 
9.  63  950 
9.  63  976 
9.64  002 
9.64  028 

26 
26 
26 
26 

9.68  497 
9.  68  529 
9.  68  561 
9.68  593 
9.  68  626 

32 
32 
32 
33 

0.31  503 
0.31  471 
0.  31  439 
0.31  407 
0.31  374 

9.  95  427 
9.  95  421 
9.  95  415 
9.  95  409 
9.  95  403 

6 
6 
6 
6 

10 

9 

8 
7 
6 

16  40 
36 
32 
28 
24 

43  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.64  054 
9.64  080 
9.64  106 
9.64  132 
9.64  158 

26 
26 
26 
26 

9.68  658 
9.68  690 
9.68  722 
9.68  754 
9.  68  786 

32 
32 
32 
32 

0.31  342 
0.31  310 
0.31  278 
0.31  246 
0.  31  214 

9.  95  397 
9.  95  391 
9.  95  384 
9.  95  378 
9.  95  372 

6 
7 
6 
6 

5 
4 
3 
2 
1 

16  20 
16 
12 
8 
4 

44   0 

60 

9.64  184 

9.  68  818 

0.31  182 

9.95  366 

0 

16   0 

L.  Cos. 

d. 

L.  Cotg. 

C.d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

64C 


174  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  26° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

44   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  64  184 
9.64210 
9.  64  236 
9.  64  262 
9.  64  288 

26 
26 
26 
26 
25 

9.  68  818 
9.68850 
9.  68  882 
9.  68  914 
9.  68  946 

32 
32 
32 

32 
32 

0.31  182 
0.31  150 
0.31  118 
0.  31  086 
0.  31  054 

9.  95  366 
9.  95  360 
9.  95  354 
9.  95  348 
9.  95  341 

6 
6 
6 

7 
ft 

60 

59 

58 
57 
56 

16   0 
56 
52 
48 
44 

44   20 
24 

28 
32 
36 

5 
6 

7 
8 
9 

9.64  313 
9.64  339 
9.  64  365 
9.  64  391 
9.  64  417 

26 
26 
26 
26 
25 

9.  68  978 
9.  69  010 
9.  69  042 
9.  69  074 
9.69  106 

32 
32 
32 
32 
32 

0.31  022 
0.30  990 
0.  30  958 
0.  30  926 
0.  30  894 

9.  95  335 
9.  95  329 
9.  95  323 
9.  95  317 
9.  95  310 

6 
6 
6 

7 
fi 

55 
54 
53 
52 
51 

15  40 
36 
32 
28 
24 

44   40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  64  442 
9.  64  468 
9.  64  494 
9.  64  519 
9.64  545 

26 
26 
25 
26 
26 

9.  69  138 
9.  69  170 
9.  69  202 
9.  69  234 
9.  69  266 

32 
32 
32 
32 
32 

0.  30  862 
0.  30  830 
0.  30  798 
0.  30  766 
0.  30  734 

9.95  304 
9.  95  298 
9.  95  292 
9.95286 
9.  95  279 

6 
6 
6 

fi 

50 

49 
48 
47 
46 

15  20 
16 
12 
8 
4 

45   0 
4 

8 
12 
16 

15 
16 
17 
18 
19 

9.  64  571 
9.64  596 
9.64  622 
9.  64  647 
9.  64  673 

25 

26 
25 
26 
25 

9.  69  298 
9.  69  329 
9.  69  361 
9.  69  393 
9.  69  425 

31 
32 
32 
32 
32 

0.  30  702 
0.  30  671 
0.  30  639 
0.  30  607 
0.  30  575 

9.  95  273 
9.  95  267 
9.  95  261 
9.  95  254 
9.  95  248 

6 
6 

6 
6 

45 
44 
43 
42 
41 

15   0 
56 

52 
48 
44 

45   20 

24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  64  698 
9.  64  724 
9.  64  749 
9.  64  775 
9.64  800 

26 
25 
26 
25 
26 

9.  69  457 
9.  69  488 
9.  69  520 
9.  69  552 
9.69  584 

31 
32 
32 
32 

31 

0.  30  543 

0.  30  512 
0.30  480 
0.  30  448 
0.30  116 

9.  95  242 
9.  95  236 
9.  95  229 
9.  95  223 
9.  95  217 

6 

6 
6 
6 

40 

39 
38 
37 
36 

14  40 
36 
32 
28' 
24 

45   40 
44 
48 
52 
56 

25 
26 
27 
28 
29 

9.  64  826 
9.64  851 
9.  64  877 
9.64  902 
9.64927 

25 
26 
25 
25 
26 

9.  69  615 
9.  69  647 
9.  69  679 
9.  69  710 
9.  69  742 

32 
32 
31 
32 
32 

0.30  385 
0.  30  353 
0.  30  321 
0.  30  290 
0.30258 

9.  95  211 
9.  96  204 
9.  95  198 
9.  95  192 
9.95  185 

7 
6 
6 
7 
6 

35 
34 
33 
32 
31 

14  20 
16 
12 

8 
4 

46   0 

4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  64  953 

9.  64  978 
9.  65  003 
9.  65  029 
9.65  054 

25 
25 
26 
25 
25 

9.69774 
9.  69  805 
9.  69  837 
9.  69  868 
9.69  900 

31 
32 
31 
32 
32 

0.30  226 
0.  30  195 
0.  30  163 
0.  30  132 
0.30  100 

9.  95  179 
9.  95  173 
9.  95  167 
9.  95  160 
9.95  154 

6 
6 

7 
6 
6 

30 

29 
28 
27 
26 

14   0 

56 
52 
48 
44 

46   20 

24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  65  079 
9.65  104 
9.65130 
9.65  155 
9.65  180 

25 

26 
25 
25 
25 

9.  69  932 
9.  69  963 
9.  69  995 
9.  70  026 
9.  70  058 

31 
32 
31 
32 
31 

0.30  068 
0.  30  037 
0.30  005 
0.  29  974 
0.  29  942 

9.  95  148 
9.  95  141 
9.95  135 
9.95  129 
9.  95  122 

7 
6 
6 
7 
6 

25 
24 
23 
22 
21 

13  40 
36 
32 
28 
24 

46   40 

44 
48 
52 
56 

40 

41 
42 
43 
44 

9.65  205 
9.65  230 
9.65  255 
9.  65  281 
9.  65  306 

25 
25 
26 
25 
26 

9.  70  089 
9.  70  121 
9.  70  152 
9.  70  184 
9.  70  215 

32 
31 
32 
31 
32 

0.29  911 
0.  29  879 
0.  29  848 
0.29816 
0.29  785 

9.  95  116 
9.95  110 
9.  95  103 
9.  95  097 
9.95  090 

6 
7 
6 
7 
6 

20 

19 
18 
17 
16 

13  20 
16 
12 
8 
4 

47   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.65  331 
9.65356 
9.  65  381 
9.  65  406 
9.  65  431 

25 
25 
25 
25 
25 

9.  70  247 
9.  70  278 
9.  70  309 
9.  70  341 
9.  70  372 

31 
31 
32 
31 
32 

0.29  753 
0.  29  722 
0.  29  691 
0.29  659 
0.29  628 

9.  95  084 
9.  95  078 
9.  95  071 
9.95  065 
9.  95  059 

6 

7 
6 
6 
7 

15 
14 
13 
12 
11 

13   0 
56 
52 
48 
44 

47   20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.65  456 
9.  65  481 
9.65  506 
9.  65  531 
9.65  556 

25 
25 
25 
25 
24 

9.  70  404 
9.  70  435 
9.  70  466 
9.  70  498 
9.  70  529 

31 
31 
32 
31 
31 

0.29  596 
0.29  565 
0.  29  534 
0.29  502 
0.29471 

9.  95  062 
9.  95  046 
9.  95  039 
9.  95  033 
9.  95  027 

6 
7 
6 
6 

7 

10 

9 

8 
7 
6 

12  40 
36 
32 
28 
24 

47   40 

44 

56 

55 
56 
57 
58 
59 

9.  65  58Q 
9.65  605 
9.65  630 
9.65  655 
9.65  680 

25 
25 
25 
25 
25 

9.  70  560 
9.  70  592 
9.  70  623 
9.70  654 
9.70  685 

32 
31 
31 
31 
32 

0.  29  440 
0.29  408 
0.  29  377 
0.  29  346 
0.29  315 

9.  95  020 
9.  95  014 
9.  95  007 
9.  95  001 
9.  94  995 

6 
7 
6 
6 
7 

5 
4 
3 
2 
1 

12  20 
16 
12 
8 
4 

48   0 

60 

9.  65  705 

9.  70  717 

0.  29  283 

9.94  988 

0 

12   0 

L.Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

63° 


GEOGRAPHIC'   TABLES    AND   FORMULAS.  175 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
lh  27° 


m. 

i 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

48   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.65  705 

y.  CM  7-_»> 

9.65  754 
9.  65  779 
9.  65  804 

24 
25 
25 
25 

9.  70  717 

9.  70  748 
9.  70  779 
9.  70  810 
9.  70  841 

31 
31 
31 
31 

0.29  283 
0.  29  252 
0.  29  221 
0.  29  190 
0.29  159 

9.  94  988 
9.  94  982 
9.  94  975 
9.  94  969 
9.  94  962 

6 
7 
6 

60 

59 

58 

57 
50 

12   0 
56 
52 
48 
44 

48  20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  65  828 
9.65  853 
9.  65  878 
9.65  902 
9.65  927 

25 
25 
24 
25 

9.  70  873 
9.70  904 
9.  70  935 
9.  70  966 
9.  70  997 

31 
31 
31 
31 

0.29  127 
0.  29  096 
0.  29  065 
0.  29  034 
0.  29  003 

9.  94  956 
9.  94  949 
9.94  943 
9.  94  936 
9.  94  930 

7 
6 

6 

7 

55 
54 
53 
52 
51 

11  40 
36 
32 
28 
24 

48  40 
44 
48 
•V2 
56 

10 

11 
12 
13 

14 

9.65  952 
9.  65  976 
9.  66  001 
9.66  025 
9.66  050 

24 

25 
24 
25 

9.  71  028 
9.71  059 
9.71  090 
9.  71  121 
9.  71  153 

31 
31 
31 
32 

0.  28  972 
0.  28  941 
0.  28  910 
0.  28  879 
0.  28  847 

9.  94  923 
9.  94  917 
9.94  911 
9.  94  904 
9.  94  898 

6 
6 

7 
6 

7 

50 

49 
48 
47 
46 

11  20 
16 
12 
8 
4 

49   0 
4 

8 
12 
16 

15 
16 
17 

18 
19 

9.  66  075 
9.  66  099 
9.  66  124 
9.  66  148 
9.  66  173 

24 
25 
24 
25 

9.71  184 
9.  71  215 
9.  71  246 
9.71  277 
9.71  308 

31 
31 
31 
31 

0.28  816 
0.  28  785 
0.  28  754 
0.  28  723 
0.  28  692 

9.  94  891 
9.  94  885 
9.  94  878 
9.  94  871 
9.  94  865 

6 

7 
7 
6 

45 
44 
43 
42 
41 

11   0 
56 
52 

48 
44 

49  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  66  197 
9.66  221 
9.  66  246 
9.  66  270 
9.66  295 

24 
25 
24 
25 

9.  71  339 
9.71  370 

'.'.71  mi 
9.  71  431 
9.71  462 

31 
31 
30 
31 

0.2S  tilil 
0.  28  630 
0.28  599 
0.  28  569 
0.  28  538 

9.94  858 
9.94  852 
9.  94  845 
9.94839 
9.  94  832 

6 

7 
6 

7 

40 

39 
38 
37 
36 

10  40 
36 
32 
28 
24 

49  40 
44 

48 
52 
56 

25 

26 
27 
28 
29 

9.  66  319 
9.66  343 
9.  66  368 
9.  66  392 
9.66  416 

24 
25 
24 
24 

9.  71  493 
9.  71  524 
9.71  555 
9.  71  586 
9.71  617 

31 
31 
31 
31 

0.  28  507 
0.  28  476 
0.28  445 
0.  28  414 
0.28  383 

9.  94  826 
9.  94  819 
9.  94  813 
9.  94  806 
9.94  799 

7 
6 

7 

7 

35 

34 
33 
32 
31 

10  20 
16 
12 

8 
4 

50   0 
4 
8 
12 
16 

30 

31 
82 

33 
34 

<>.  66  441 
9.  66  465 
9.  66  489 
9.  66  513 
9.  66  537 

24 
24 

24 
24 

OK 

9.  71  648 
9.  71  679 
9.71  709 
9.  71  740 
9.71  771 

31 
30 
31 
31 

0.  28  352 
0.  28  321 
0.  28  291 
0.28  260 
0.28  229 

9.  94  793 
9.94  786 
9.  94  780 
9.  94  773 
9.  94  767 

7 
6 

7 
6 

30 

29 
28 
27 
26 

10   0 

56 
52 
48 
44 

50  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.66  562 
9.66  586 
9.  66  610 
9.66  634 
9.66  658 

24 
24 
24 
24 

9.71  802 
9.  71  833 
9.  71  863 
9.71  894 
9.  71  925 

31 
30 
31 
31 

0.28  198 
0.28  167 
0.  28  137 
0.28  106 
0.28075 

9.  94  760 
9.  94  753 
9.  94  747 
9.94  740 
9.  94  734 

7 
6 
7 
6 

25 
24 
23 
22 
21 

9  40 
36 
32 

28 
24 

50  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  66  682 
9.66  706 
9.  66  731 
9.  66  755 
9.  66  779 

24 
25 
24 

24 

9.  71  955 
9.71  986 
9.  72  017 
9.  72  048 
9.  72  078 

31 
31 
31 
30 

0.28045 
0.  28  014 
0.  27  983 
0.27  952 
0.27  922 

9.  94  727 
9.  94  720 
9.  94  714 
9.  94  707 
9.  94  700 

6 

7 

7 

20 

19 
18 
17 
16 

9  20 
16 
12 

8 
4 

51   0 
4 

8 
12 
16 

45 
46 
47 

48 
49 

9.66803 
9.  66  827 
9.  66  851 
9.  66  875 
9.  66  899 

24 
24 
24 

24 

9.72  109 
9.  72  140 
9.  72  170 
9.'  72  201 
9.  72  231 

31 
30 
31 
30 

0.  27  891 
0.  27  860 
0.  27  830 
0.  27  799 
0.  27  769 

9.94  694 
9.  94  687 
9.94  680 
9.  94  674 
9.  94  667 

7 
7 
6 

7 

15 
14 
13 
12 
11 

9   0 
56 
52 

48 
44 

51  20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.66  922 
9.  66  946 
9.  66  970 
9.66  994 
9.  67  018 

24 
24 
24 
24 

9.  72  262 
9.  72  293 
9.  72  323 
9.  72  354 
9.72  384 

31 
30 
31 
30 

0.27  738 
0.27  707 
0.  27  677 
0.  27  646 
0.  27  C16 

9.  94  660 
9.  94  654 
9.  94  647 
9.  94  640 
9.  94  634 

6 

7 
7 
6 

10 

9 
8 
7 
6 

8  40 
36 
32 

28 
24 

51  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

(.).f)7  012 
9.67  066 
9.67  090 
9.  67  113 
9.  67  137 

24 
24 

23 
24 

9.  72  415 
9.72  445 
9.  72  476 
9.  72  506 
9.  72  537 

30 
31 
30 
31 

0.  27  585 
0.  27  f>.r>5 
0.  27  524 
5.  27  494 
0.  27  463 

9.  94  627 
9.94  620 
9.  94  614 
9.  94  607 
9.94600 

7 
6 

7 

7 

5 
4 
3 
2 

1 

8  20 
16 
12 

8 
1 

52   0 

60 

9.  67  161 

9.  72  567 

0.  27  433 

9.  94  593 

0 

8  .0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

62° 


176  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
lh  28° 


m.   s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos.  ' 

d. 

52   0 
4 
8 
12 
16 

0 

1 

2 
3 

4 

9.  67  161 
9.  67  185 
9.  67  208 
9.  67  232 
9.  67  256 

24 
23 
24 
24 
24 

9.  72  567 
9.  72  598 
9.  72  628 
9.  72  659 
9.  72  689 

31 
30 
31 
30 
31 

0.  27  433 
0.27  402 
0.27  372 
0.  27  341 
0.27  311 

9.  94  593 
9.  94  587 
9.  94  580 
9.94573 
9.  94  567 

6 

7 
7 
6 
7 

60 

59 

58 
57 
56 

8   0 
56 
52 
48 
44 

52  20 
24 
28 
32 
36 

5 
6 
7 

8 
9 

9.  67  280 
9.  67  303 
9.  67  327 
9.  67  350 
9.  67  374 

23 
24 
23 
24 
24 

9.  72  720 
9.  72  750 
9.  72  780 
9.  72  811 
9.  72  841 

30 
30 
31 
30 
31 

0.  27  280 
0.27  250 
0.27  220 
0.  27  189 
0.27  159 

9.  94  560 
9.  94  553 
9.  94  646 
9.  94  540 
9.94  533 

7 

7 
6 
7 
7 

55 
54 
53 
52 
51 

7  40 
36 
32 
28 
24 

52  40 
44 
48 
52 
66 

10 

11 

12 
13 
14 

9.  67  398 
9.  67  421 
9.67  445 
9.  67  468 
9.  67  492 

23 

24 
23 
24 
23 

9.  72  872 
9.  72  902 
9.  72  932 
9.  72  963 
9.  72  993 

30 
30 
31 
30 
30 

0.27  128 
0.  27  098 
0.  27  068 
0.  27  037 
0.  27  007 

9.  94  526 
9.94  519 
9.  94  513 
9.94  506 
9.  94  499 

7 
6 
7 
7 

7 

50 

49 

48 
47 
46 

7  20 
16 
12 
8 
4 

53   0 

4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  67  515 
9.  67  539 
9.  67  662 
9.  67  586 
9.  67  609 

24 
23 
24 
23 
24 

9.73  023 
9.73  054 
9.  73  084 
9.  73  114 
9.  73  144 

31 
30 
30 
30 
31 

0.26  977 
0.  26  946 
0.  26  916 
0.26  886 
0.  26  856 

9.94  492 
9.94485 
9.  94  479 
9.  94  472 
9.  94  495 

7 
6 
7 

7 

45 
44 
43 
42 
41 

7   0 
56 

52 
48 
44 

53  20 
24 

28 
32 
36 

20 

21 
22 
23 
24 

9.67  633 
9.  67  656 
9.  67  680 
9.  67  703 
9.  67  726 

23 
24 
23 
23 

24 

9.  73  175 
9.  73  20§ 
9.  73  235 
9.  73  265 
9.73  295 

30 
30 
30 
30 
31 

0.26  825 
0.  26  795 
0.  26  765 
0.  26  735 
0.  26  705 

9.  94  458 
9,  94  451 
9.94  445 
9.  94  438 
9.  94  431 

7 
6 
7 

7 
7 

40 

39 
38 
37 
36 

6  40 
36 
32 

28 
24 

53  40 
44 
48 
52 
66 

25 
26 
27 
28 
29 

9.67  750 
9.  67  773 
9.67  796 
9.  67  820 
9.67  843 

23 
23 
24 
23 
23 

9.  73  326 
9.  73  356 
9.  73  386 
9.  73  416 
9.  73  446 

30 
30 
30 
30 

30 

0.  26  674 
0.  26  644 
0.  26  614 
0.26  584 
0.26  554 

9.  94  424 
9.94  417 
9.  94  410 
9.  94  404 
9.  94  397 

7 
7 
6 

7 
7 

35 
34 
33 
32 
31 

6  20 
16 
12 

8 
4 

54   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  67  866 
9.  67  890 
9.  67  913 
9.  67  936 
9.  67  959 

24 
23 
23 
23 
23 

9.  73  476 
9.  73  507 
9.  73  537 
9.  73  567 
9.  73  597 

31 
30 
30 
30 

30 

0.  26  524 
0.  26  493 
0.  26  463 
0.  26  433 
0.  26  403 

9.  94  390 
9.  94  383 
9.94  376 
9.  94  369 
9.  94  362 

7 
7 
7 
7 
7 

30 

29 

28 
27 
26 

6   0 
56 
52 

48 
44 

64  20 
24 

28 
32 
36 

35 
36 
37 
38 
39 

9.  67  982 
9.68  006 
9.  68  029 
9.  68  052 
9.  68  075 

24 
23 
23 
23 
23 

9.  73  627 
9.  73  657 
9.  73  687 
9.  73  717 
9.  73  747 

30 
30 
30 
30 
30 

0.26  373 
0.  26  343 
0.26  313 
0.26  283 
0.  26  253 

9.94  355 
9.94  349 
9:  94  342 
9.  94  335 
9.  94  328 

6 

7 

7 
7 
7 

25 
24 
23 
22 
21 

5  40 
36 
32 
28 
24 

54  40 

44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  68  098 
9.  68  121 
9.  68  144 
9.  68  167 
9.68190 

23 
23 
23 
23 
23 

9.  73  777 
9.  73  807 
9.  73  837 
9.  73  867 
9.  73  897 

30 
30 
30 
30 
30 

0.26  223 
0.  26  193 
0.26  163 
0.  26  133 
0.26  103 

9.94  321 
9.94  314 
9.  94  307 
9.94  300 
9.  94  293 

7 

7 
7 

7 

7 

20 

19 
18 
17 
16 

5  20 
16 
12 

8 
4 

55   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

9.  68  213 
9.  68  237 
9.  68  260 
9.  68  283 
9.  68  305 

24 
23 
23 
22 
23 

9.  73  927 
9.  73  957 
9.  73  987 
9.  74  017 
9.  74  047 

30 
30 
30 
30 
30 

0.  26  073 
0.  26  043 
0.  26  013 
'  0.25  983 
0.25  953 

9.  94  286 
9.  94  279 
9.  94  273 
9.  94  266 
9.  94  259 

7 
6 

7 
7 
7 

15 
14 
13 
12 
11 

5   0 
56 
52 
48 
44 

55  20 
24 
28 
32 
36 

50 

51 

52 
53 
54 

9.  68  328 
9.  68  351 
9.  68  374 
9.  68  397 
9.  68  420 

23 

23 
23 
23 
23 

9.  74  077 
9.  74  107 
9.  74  137 
9.  74  166 
9.  74  196 

30 
30 
29 
30 
30 

0.  25  923 
0.  25  893 
0.  25  863 
0.  25  834 
0.  25  804 

9.  94  252 
9.  94  245 
9.  94  238 
9.94  231 
9.94  224 

7 
7 
7 

7 
7 

10 

9 
8 

7 
6 

4  40 
36 

32 
28 
24 

55  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  68  443 
9.68466 
9.  68  489 
9.  68  512 
9.  68  634 

23 
23 
23 
22 
23 

9.  74  226 
9.  74  256 
9.  74  286 
9.  74  316 
9.  74  345 

30 
30 
30 
29 
30 

0.25  774 
0.  25  744 
0.  25  714 
0.  25  684 
0.25  655 

9.94  217 
9.  94  210 
9.  94  203 
9.94  196 
9.  94  189 

7 

7 
7 
7 
7 

5 

4 
3 
2 
1 

4  20 
16 
12 
8 
4 

66   0 

60 

9.  68  657 

9.  74  375 

0.25626 

9.  94  182 

0 

4   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.   s. 

61° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  177 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

lh  29° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

56   0 
4 
8 
12 
16 

0 

1 
2 

4 

9.68  557 
9.  68  580 
9.68  603 
9.  68  625 
9.  68  648 

23 
23 
22 
23 
23 

9.  74  375 
9.  74  405 
9.  74  435 
9.  74  465 
9.  74  494 

30 
30 
30 
29 
30 

0.  25  625 
0.  25  595 
0.  25  565 
0.  25  535 
0.25  506 

9.  94  182 
9.  94  175 
9.  94  168 
9.  94  161 
9.  94  154 

7 
7 
7 

7 
7 

60 

59 
58 
57 
56 

4   0 

56 
52 
48 
44 

56  20 
24 
28 
32 
36 

5 

6 

7 
8 
9 

9.  68  671 
9.  68  694 
9.  68  716 
9.  68  73o 
9.  68  762 

23 
22 
23 
23 

22 

9.  74  524 
9.74  554 
9.74  583 
9.  74  613 
9.  74  643 

30 
29 
30 
30 
30 

0.  25  476 
0.  25  446 
0.  25  417 
0.  25  387 
0.  25  357 

9.  94  147 
9.  94  140 
9.94  133 
9.  94  126 
9.  94  119 

7 
7 
7 
7 
7 

55 
54 
53 
52 
51 

3  40 
36 
32 

28 
24 

56  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  68  784 
9.  68  807 
9.  68  829 
9.68  852 
9.  68  875 

23 
22 
23 
23 
22 

9.  74  673 
9.  74  702 
9.  74  732 
9.  74  762 
9.  74  791 

29 
30 
30 
29 
30 

0.  25  327 
0.  25  298 
0.  25  268 
0.25  238 
0.  25  209 

9.  94  112 
9.  94  105 
9.  94  098 
9.  94  090 
9.  94  083 

7 
7 
8 

7 

50 

49 
48 
47 
-  46 

3  20 
16 
12 

8 
4 

57   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  68  897 
9.  68  920 
9.  68  942 
9.  68  965 
9.68  987 

23 
22 
23 
22 
23 

9.  74  821 
9.  74  851 
9.74  880 
9.  74  910 
9.  74  939 

30 
29 
30 
29 
30 

0.  25  179 
0.  25  149 
0.25  120 
0.  25  090 
0.  25  061 

9.  94  076 
9.  94  069 
9.  94  062 
9.  94  055 
9.  94  048 

7 
7 
7 
7 
7 

45 
44 
43 
42 
41 

3   0 
56 
52 
48 
44 

57  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  69  010 
9.  69  032 
9.  69  055 
9.  69  077 
9.  69  100 

22 
23 
22 
23 
22 

9.  74  969 
9.  74  998 
9.75  028 
9.  75  058 
9.  75  087 

29 
30 
30 
29 
30 

0.  25  031 
0.  25  002 
0.  24  972 
0.  24  942 
0.  24  913 

9.  94  041 
9.94034 
9.  94  027 
9.  94  020 
9.  94  012 

7 
7 
7 
8 
7 

40 

39 
38 
37 
36 

2  40 
36 
32 

28 
24 

57  40 
44 
48 
52 
56 

25 

26 
27 
28 
29 

9.  69  122 
9.  69  144 
9.  69  167 
9.  69  189 
9.  69  212 

22 
23 
22 
23 
22 

9.75  117 
9.  75  146 
9.  75  176 
9.  75  205 
9.  75  235 

29 
30 
29 
30 
29 

0.  24  883 
0.  24  854 
0.  24  824 
0.  24  795 
0.  24  765 

9.  94  005 
9.  93  998 
9.  93  991 
9.  93  984 
9.  93  977 

7 
7 
7 
7 
7 

35 
34 
33 
32 
31 

2  20 
16 
12 
8 
4 

58   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.69  234 
9.  69  2.56 
9.  69  279 
9.  69  301 
9.  69  323 

22 
23 
22 
22 
22 

9.  75  264 
9.75  294 
9.75  323 
9.  75  353 
9.  75  382 

30 
29 
30 
29 
29 

0.24736 
0.  24  706 
0.  24  677 
0.24  647 
0.  24  618 

9.  93  970 
9.  93  96? 
9.  93  955 
9.  93  948 
9.  93  941 

7 
8 
7 
7 
7 

30 

29 
28 
27 
26 

2   0 
56 
52 
48 
44 

58  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  69  345 
9.  69  368 
9.  69  390 
9.  69  412 
9.  69  434 

23 
22 
22 
22 
22 

9.  75  411 
9.  75  441 
9.  75  470 
9.  75  500 
9.  75  529 

30 
29 
30 
29 
29 

0.  24  589 
0.24  559 
0.  24  530 
0.  24  500 
0.24  471 

9.  93  934 
9.  93  927 
9.  93  920 
9.  93  912 
9.  93  905 

7 
7 
8 
7 
7 

25 
24 
23 
22 
21 

1  40 
36 
32 

28 
24 

58  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.69  456 
9.  69  479 
9.  69  501 
9.  69  523 
9.  69  545 

23 

22 
22 
22 
22 

9.  75  558 
9.75  588 
9.  75  617 
9.  75  647 
9.  75  676 

30 
29 
30 
29 
29 

0.  24  442 
0.  24  412 
0.  24  383 
0.  24  353 
0.24  324 

9.  93  898 
9.  93  891 
9.  93  884 
9.  93  876 
9.  93  869 

7 
7 
8 
7 
7 

20 

19 
18 
17 
16 

1  20 
16 
12 

8 
4 

59   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

9.  69  567 
9.  69  589 
9.  69  611 
9.  69  633 
9.  69  655 

22 
22 
22 
22 

22 

9.  75  705 
9.  75  735 
9.  75  764 
9.  75  793 
9.  75  822 

30 
29 
29 
29 
30 

0.  24  29£ 
0.24  265 
0.  24  236 
0.  24  207 
0.  24  178 

9.  93  862 
9.  93  855 
9.  93  847 
9.  93  840 
9.  93  833 

7 
8 

7 
7 
7 

15 
14 
13 
12 
11 

1   0 
56 
52 
48 
44 

59  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  69  67.7 
9.  69  699 
9.  69  721 
9.  69  743 
9.  69  765 

22 

22 
22 
22 
22 

9.  75  852 
9.  75  881 
9.  75  910 
9.  75  939 
9.  75  969 

29 
29 
29 
30 
29 

0.  24  148 
0.24  119 
0.  24  090 
0.  24  061 
0.  24  031 

9.  93  826 
9.  93  819 
9.  93  811 
9.  93  804 
9.  93  797 

7 
8 

7 
7 
8 

10 

9 
8 
7 
6 

0  40 
36 
32 
28 
24 

59  40 
44 

48 
52 
56 

55 
56 
57 

58 
59 

9.  69  787 
9.69  809 
9.  69  831 
9.  69  853 
9.  69  875 

22 
22 
22 
22 
22 

9.  75  998 
9.  76  027 
9.  76  056 
9.  76  086 
9.  76  115 

29 
29 
30 
29 
29 

0.  24  002 
0.  23  973 
0.  23  944 
0.23  914 
0.  23  885 

9.  93  789 
9.  93  782 
9.  93  775 
9.  93  768 
9.  93  760 

7 
7 
7 
8 
7 

5 
4 
3 

2 
1 

0  20 
16 
12 

8 

4 

60   0 

60 

9.  69  897 

9.  76  144 

0.23  856 

9.  93  753 

0 

0   0 

L.Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

60° 


46061—08 12 


178  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  30° 


m.  s. 

t 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

0   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  69  897 
9.69  919 
9.  69  941 
9.  69  963 
9.  69  984 

22 
22 
22 
21 
22 

9.  76  144 
9.  76  173 
9.  76  202 
9.  76  231 
9.  76  261 

29 
29 
29 
30 
29 

0.  23  856 
0.  23  827 
0.  23  798 
0.  23  769 
0.23  739 

9.  93  753 
9.  93  746 
9.  93  738 
9.  93  731 
9.  93  724 

7 
8 
7 
7 
7 

60 

59 
58 
57 
56 

60   0 
56 
52 
48 
44 

0  20 
24 
28 
32 
36 

5 
0 

7 
8 
9 

9.  70  006 
9.  70  028 
9.  70  050 
9.  70  072 
9.  70  093 

22 
22 
22 
21 
22 

9.76  290 
9.  76  319 
9.  76  348 
9.  76  377 
9.  76  406 

29 
29 
29 
29 
29 

0.  23  710 
0.  23  681 
0.23  652 
0.  23  623 
0.23  594 

9.  93  717 
9.  93  709 
9.  93  702 
9.  93  695 
9.  93  687 

8 

7 
7 
8 
7 

55 
54 
53 
52 
51 

59  40 
36 
32 
28 
24 

0  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  70  115 
9.  70  137 
9.  70  159 
9.  70  180 
9.  70  202 

'  22 
22 
21 

22 

22 

9.  76  435 
9.  76  464 
9.  76  493 
9.  76  522 
9.  76  551 

29 
29 
29 
29 
29 

0.  23  565 
0.  23  636 
0.23  507 
0.23  478 
0.  23  449 

9.  93  680 
9.93  673 
9.  93  665 
9.  93  658 
9.  93  650 

7 
•  8 
7 
8 
7 

50 

49 
48 
47 
46 

59  20 
16 
12 
8 
4 

1   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  70  224 
9.  70  245 
9.  70  267 
9.  70  288 
9.  70  310 

21 
22 
21 
22 

22 

9.76  580 
9.  76  609 
9.  76  639 
9.  76  668 
9.  76  697 

29 
30 
29 
29 

28 

0.  23  420 
0.  23  391 
0.  23  361 
0.23  332 
0.23  303 

9.  93  643 
9.  93  636 
9.  93  628 
9.  93  621 
9.  93  614 

7 
8 

7 
7 
8 

45 
44 
43 
42 
41 

59   0 
56 
52 

48 
44 

1  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.70  332 
9.  70  353 
9.  70  375 
9.  70  396 
9.  70  418 

21 
22 
21 
22 
21 

9.  76  725 
9.  76  754 
9.  76  783 
9.  76  812 
9.  76  841 

29 
29 
29 
29 
29 

0.  23  275 
0.  23  246 
0.  23  217 
0.  23  188 
0.  23  159 

9.93  606 
9.  93  599 
9.  93  591 
9.  93  684 
9.  93  577 

7 
8 
7 
7 
8 

40 

39 

38 
37 
36 

58  40 
36 
32 
28 
24 

1  40 
44 

48 
52 
56 

25 
26 

27 
28 
29 

9.  70  439 
9.  70  461 
9.  70  482 
9.  70  504 
9.  70  525 

22 
21 
22 
21 
22 

9.  76  870 
9.  76  899 
9.  76  928 
9.  76  957 
9.76  986 

29 
29 
29 
29 

29 

0.23  130 
0.  23  101 
0.  23  072 
0.  23  043 
0.  23  014 

9.  93  569 
9.  93  562 
9.  93  554 
9.  93  547 
9.  93  539 

7 
8 
7 
8 

35 
34 
33 
32 
31 

58  20 
16 
12 
8 
4 

2   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  70  547 
9.  70  568 
9.  70  590 
9.70  611 
9.  70  633 

21 
22 
21 
22 
21 

9.  77  015 
9.  77  044 
9.  77  073 
9.77  101 
9.  77  130 

29 
29 
28 
29 
29 

0.  22  985 
0.  22  956 
0.  22  927 
0.  22  899 
0.  22  870 

9.  93  532 
9.  93  525 
9.  93  517 
9.  93  510 
9.  93  502 

7 
8 

8 

7 

30 

29 

28 
27 
'16 

58   0 
56 
52 
48 
44 

2  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  70  654 
9.  70  675 
9.  70  697 
9.  70  718 
9.  70  739 

21 
22 
21 
21 

22 

9.  77  159 
9.  77  188 
9.  77  217 
9.  77  246 
9.  77  274 

29 
29 
29 

28 
29 

0.  22  841 
0.  22  812 
0.22  783 
0.  22  754 
0.22  726 

9.  93  495 
9.  93  487 
9.  93  480 
9.  93  472 
9.  93  465 

8 

'  7 
8 
7 
8 

25 
24 
23 
22 

21 

57  40 
36 
32 
28 
24 

2  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  70  761 
9.  70  782 
9.  70  803 
9.  70  824 
9.  70  846 

21 
21 
21 
22 
21 

9.  77  303 
9.  77  332 
9.  77  361 
9.  7-7  390 
9.  77  418 

29 
29 
29 
28 
29 

0.  22  697 
0.  22  668 
0.22  639 
0.  22  610 
0.  22  582 

9.  93  457 
9.  93  450 
9.  93  442 
9.  93  435 
9.  93  427 

7 
8 
7 
8 

7 

20 

19 
18 
17 
16 

57  20 
16 
12 
8 
4 

3   0 
4 

8 
12 
16 

45 
46 
47 
48 
49 

9.  70  867 
9.  70  888 
9.  70  909 
9.  70  931 
9.  70  952 

21 
21 
22 
21 
21 

9.  77  447 
9.  77  476 
9.  77  505 
9.  77  533 
9.  77  562 

29 
29 
28 
29 
29 

0.  22  553 
0.  22  524 
0.  22  495 
0.  22  467 
0.22  438 

9.  93  420 
9.  93  412 
9.  93  405 
9.  93  397 
9.  93  390 

8 
7 
8 
7 
8 

15 
14 
13 
12 
11 

57   0 
56 
52 
48 
44 

3  20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.  70  973 
9.  70  994 
9.  71  015 
9.  71  036 
9.  71  058 

21 
21 
21 
22 
21 

9.  77  591 
9.  77  619 
9.77  648 
9.77  677 
9.  77  706 

28 
29 
29 
29 

28 

0.  22  409 
0.  22  381 
0.  22  352 
0.  22  323 
0.  22  294 

9.  93  382 
9.  93  375 
9.  93  367 
9.  93  360 
9.93  352 

7 
8 
7 
8 
8 

10 

9 

8 
7 
6 

56  40 
36 
32 
28 
24 

3  40 
44 

48 
52 
56 

55 
56 

57 
58 
59 

9.  71  079 
9.71  100 
9.71  121 
9.71  142 
9.71  163 

21 
21 
21 
21 
21 

9.  77  734 
9.  77  763 
9.77  791 
9.  77  820 
9.  77  849 

29 
28 
29 
29 

28 

0-22  266 
0.  22  237 
0.  22  209 
0.  22  180 
0.  22  151 

9.  93  344 
9.  93  337 
9.  93  329 
9.  93  322 
9.  93  314 

7 
8 
7 
8 

5 
4 
3 
2 
1 

56  20 
16 
12 
8 
4 

4   0 

60 

9.71  184 

9.  77  877 

0.22  123 

9.  93  307 

0 

56   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin 

d. 

/ 

m.  s. 

59° 


GEOGRAPHIC  TABLES  AND  FORMULAS.          179 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

2h  31° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

4   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  71  184 
9.71  205 
9.71  226 
9.  71  247 
9.  71  268 

21 
21 
21 
21 
21 

9.  77  877 
9.  77  906 
9.  77  935 
9.  77  963 
9.77  992 

29 
29 
28 
29 

28 

0.22  123 
0.  22  094 
0.  22  065 
0.22  037 
0.  22  008 

9.  93  307 
9.  93  299 
9.  93  291 
9.  93  284 
9.  93  276 

8 
8 
7 
8 

7 

60 

59 

58 
57 
56 

56   0 
56 
52 
48 
44 

4   20 
24 

28 
32 
36 

5 
6 
7 
8 
9 

9.71  289 
9.71  310 
9.71  331 
9.71  352 
9.  71  373 

21 
21 
21 
21 
20 

9.  78  020 
9.  78  049 
9.  78  077 
9.78  106 
9.  78  1&5 

29 
28 
29 
29 
28 

0.21  980 
0.21  951 
0.21  923 
0.21  894 
0.21  865 

9.  93  269 
9.  93  261 
9.  93  253 
9.  93  246 
9.  93  238 

8 
8 

7 
8 
8 

55 

54 
53 
52 
51 

55   40 
36 
32 
28 
24 

4   40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.71  393 
9.71  414 
9.  71  435 
9.  71  456 
9.71  477 

21 
21 
21 
21 
21 

9.78  163 
9.  78  192 
9.  78  220 
9.  78  249 
9.  78  277 

29 
28 
29 
28 
29 

0.21  837 
0.21  808 
0.21  780 
0.21  751 
0.21  723 

9.  93  230 
9.  93  223 
9.93  215 
9.  93  207 
9.93  200 

7 
8 
8 
7 
8 

50 

49 
48 
47 
46 

55   20 
16 
12 
8 
4 

5   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.71  498 
9.  71  519 
9.  71  539 
9.71  560 
9,71  581 

21 
20 
.  21 
21 
21 

9.78  306 
9.  78  334 
9.78  363 
9.  78  391 
9.  78  419 

28 
29 
28 
28 
29 

0.21  694 
0.  21  666 
0.21  637 
0.21  609 
0.  21  581 

9.93  192 
9.  93  184 
9.  93  177 
9.  93  169 
9.  93  161 

8 
7 
8 
8 

7 

45 
44 
43 
42 
41 

55   0 

56 
52 
48 
44 

5   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.71  602 
9.71  622 
9.71  643 
9.  71  664 
9.71  685 

20 
21 
21 
21 
20 

9.  78  448 
9.  78  476 
9.78  505 
9.78  533 
9.  78  562 

28 
29 
28 
29 

28 

0.21  552 
0,  21  524 
0.21  495 
0.21  467 
0.  21  438 

9.  93  154 
9.  93  146 
9.  93  138 
9.  93  131 
9.93  123 

8 
8 
7 
8 
8 

40 

39 
38 
37 
36 

54   40 
36 
32 
28 
24 

5   40 

44 
48 
52 
56 

25 
26 
27 
28 
29 

9.71  705 
9.71  726 
9.71  747 
9.  71  767 
9.71  788 

21 
21 
20 
21 
21 

9.  78  690 
9.  78  618 
9.  78  647 
9.  78  6.75 
9.  78  704 

28 
29 
28 
29 
28 

0.  21  410 
0.  21  382 
0.21  353 
0.21  325 
0.21296 

9.  93  115 
9.  93  108 
9.  93  100 
9.  93  092 
9.  93  084 

7 
8 
8 
8 
7 

35 
34 
33 
32 
31 

54   20 
16 
12 

8 
4 

6   0 
4 
b 
12 
16 

30 

31 
32 
33 
34 

9.  71  809 
9.  71  829 
9.71  850 
9.  71  870 
9.71  891 

20 
21 
20 
21 
20 

9.  78  732 

9.  78  760 
9.  78  789 
9.  78  817 
9.  78  845 

28 
29 
28 
28 
29 

0.21  268 
0.21  240 
0.21  211 
0.21  183 
0.21  155 

9.  93  077 
9.  93  069 
9.  93  061 
9.  93  053 
9.  93  046 

8 
8 
8 

7 
8 

80 

29 

28 
27 
26 

54   0 
56 
52 
48 
44 

6   20 
24 
28 
32 
36 

35 

36 
37 
38 
39 

9.  71  911 
9.71  932 
9.71  952 
9.  71  973 
9.71  994 

21 
20 
21 
21 
20 

9.  78  874 
9.78  902 
9.  78  930 
9.  78  959 
9.  78  987 

28 
28 
29 
28 
28 

0.21  126 
0.  21  098 
0.21  070 
0.  21  041 
0.  21  013 

9.  93  038 
9.  93  030 
9.  93  022 
9.  93  014 
9.93  007 

8 
8 

8 
7 
8 

25 
24 
23 
22 
21 

53   40 

36 
32 

28 
24 

6   40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  72  014 
9.  72  034 
9.  72  055 
9.  72  075 
9.72  0% 

20 

•21 
20 
21 
20 

9.  79  015 
9.  79  043 
9.  79  072 
9.  79  100 
9.79  128 

28 
29 

28 
28 
28 

0.20985 
0.  20  957 
0.  20  928 
0.  20  900 
0.  20  872 

9.92  999 
9.  92  991 
9.  92  983 
9.  92  976 
9.92  968 

8 
8 
7 
8 

8 

20 

19 
18 
17 
16 

;»:;  -ju 
16 

'   8 
4 

7   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.  72  116 
9.72  137 
9.72  157 
9.  72  177 
9.72  198 

21 
20 
20 
21 
20 

9.  79  156 
9.  79  185 
9.  79  213 
9.  79  241 
9.  79  269 

29 

28 
28 
28 
28 

0.  20  844 
0.  20  815 
0.  20  787 
0.  20  759 
0.  20  731 

9.  92  960 
9.  92  952 
9.  92  944 
9.92  936 
9.92  929 

8 
8 
8 

7 
8 

15 
14 
13 
12 
11 

53   0 

56 
52 

48 
44 

7   20 
24 
28 
32 
36 

50 

51 
62 

53 
54 

9.  72  218 
9.  72  238 
9.  72  259 
9.  72  279 
9.  72  299 

20 
21 
20 
20 
21 

9.  79  297 
9.  79  326 
9.79  354 
9.  79  382 
9.  79  410 

29 
28 
28 
28 
28 

0.  20  703 
0.  20  674 
0.  20  646 
0.20  618 
0.20  590 

9.92  921 
9.  92  913 
9.92  905 
9.  92  897 
9.92  889 

8 
8 
8 
8 
8 

10 

9 

8 
7 
6 

52   40 
36 
32 
28 
24 

7   40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  72  320 
9.  72  340 
9.72  360 
9.  72  381 
9.  72  401 

20- 
20 
21 
20 
20 

9.  79  438 
9.  79  466 
9.  79  495 
9.  79  523 
9.  79  551 

28 
29 
28 
28 
28 

0.  20  562 
0.  20  534 
0.  20  505 
0.  20  477 
0.  20  449 

9.  92  881 
9.  92  874 
9.  92  866 
9.  92  858 
9.  92  850 

7 
8 
8 
8 
8 

5 
4 
3 
2 
1 

52   20 

16 
12 
8 
4 

8   0 

60 

9.  72  421 

9.  79  579 

0.  20  421 

9.92  842 

0 

52   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

58C 


180  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  32° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

8   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  72  421 
9.  72  441 
9.  72  461 
9.  72  482 
9.72  502 

20 
20 
21 
20 
20 

9.  79  579 
9.  79  607 
9.  79  6&5 
9.  79  663 
9.  79  691 

28 
28 
28 
28 
28 

0.  20  421 
0.  20  393 
0.  20  365 
0.  20  337 
0.  20  309 

9.  92  842 
9.  92  834 
9.  92  826 
9.  92  818 
9.  92  810 

8 
8 
8 
8 

7 

60 

59 

58 
57 
56 

52   0 
56 
52 
48 
44 

8  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  72  522 

9.  72  542 
9.72  562 
9.  72  582 
9.72  602 

20 
20 
20 
20 
20 

9.  79  719 
9.  79  747 
9.  79  776 
9.  79  804 
9.  79  832 

28 
29 
28 
28 

28 

0.  20  281 
0.20  253 
0.  20  224 
0.20  196 
0.20  168 

9.  92  803 
9.  92  795 
9.  92  787 
9.  92  779 
9.  92  771 

8 
8 
8 
8 
8 

55 
54 
53 
52 
51 

51  40 
36 
32 
28 
24 

8  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  72  622 
9.  72  643 
9.72  663 
9.  72  683 
9.  72  703 

21 

20 
20 
20 
20 

9.  79  860 
9.  79  888 
9.  79  916 
9.  79  944 
9.  79  972 

28 
28 
28 
28 

28 

0.  20  140 
0.  20  112 
0.  20  084 
0.  20  056 
0.  20  028 

9.92  763 
9.  92  755 
9.  92  747 
9.  92  739 
9.  92  731 

8 
8 
8 
8 
8 

50 

49 
48 
47 
46 

51  20 
16 
12 

8 
4 

9   0 
4 
8 
12 
16 

15 
16 
17 

18 
19 

9.  72  723 
9.  72  743 
9.  72  763 
9.  72  783 
9.  72  803 

20 
20 
20 
20 

9Q 

9.80  000 
9.  80  028 
9.  80  056 
9.80084 
9.  80  112 

26 

28 
28 
.  28 
28 

0.20  000 
0.  19  972 
0.  19  944 
0.  19  916 
0.  19  888 

9.  92  723 
9.92  715 
9.92  707 
9.  92  699 
9.  92  691 

8 
8 
8 
8 
8 

45 
44 
43 
42 
41 

51   0 

56 
52 
48 
44 

9  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  72  823 
9.  72  843 
9.  72  863 
9.  72  883 
9.  72  902 

20 
20 
20 
19 
20 

9.  80  140 
9.80  168 
9.80  195 
9.  80  223 
9.  80  251 

28 
27 
28 
28 
28 

0.  19  860 
0.  19  832 
0.  19  805 
0.  19  777 
0.  19  749 

9.  92  683 
9.92  675 
9.  92  667 
9.  92  659 
9.  92  651 

8 
8 
8 
8 
8 

40 

39 
38 
37" 
36 

50  40 
36 
32 
28 
24 

9  40 

44 
48 
52 
56 

25 
26 

27 
28 
29 

9.  72  922 
9.72  942 
9.  72  962 
9.  72  982 
9.  73  002 

20 
20 
20 
20 
20 

9.  80  279 
9.  80  307 
9.  80  335 
9.  80  363 
9.  80  391 

28 
28 
28 
28 
28 

0.  19  721 
0.  19  693 
0.  19  665 
0.  19  637 
0.  19  609 

9.92  643 
9.  92  635 
9.  92  627 
9.  92  619 
9.  92  611 

8 
8 
8 
8 
8 

35 
34 
33 
32 
31 

50  20 
16 
12 

8 
4 

10   0 

4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  73  022 
9.73  041 
9.  73  061 
9.  73  081 
9.  73  101 

19 
20 
20 
20 
20 

9.  80  419 
9.  80  447 
9.80  474 
9.80  502 
9.80530 

28 
27 
28 

28 
28 

0.  19  581 
0.  19  553 
0.  19  426 
0.  19  498 
0.  19  470 

9.  92  603 
9.  92  595 
9.  92  587 
9.  92  579 
9.  92  571 

8 
8 
8 
8 

8 

30 

29 
28 
27 
26 

50   0 
56 
52 
48 
44 

10  20 
24 
28 
32 
36 

35 
36 
37 
38 
-  39 

9.  73  121 
9.  73  140 
9.  73  160 
9.  73  180 
9.  73  200 

19 
20 
20 
20 
19 

9.80  558 
9.80  586 
9.  80  614 
9.  80  642 
9.  80  669 

28 
28 
28 
27 
28 

0.  19  442 
0.  19  414 
0.  19  386 
0.  19  358 
0.  19  331 

9.  92  563 
9.  92  555 
9.  92  546 
9.  92  538 
9.  92  530 

8 
9 

8 
8 
8 

25 
24 
23 
22 
21 

49  40 
36 
32 
28 
24 

10  40 
44 
48 
52 
56 

40 

41 

43 
44 

9.  73  219 
9.  73  239 
9.  73  259 
9.  73  278 
9.73  298 

20 
20 
19 
20 
20 

9.  80  697 
9.80  725 
9.  80  753 
9.  80  781 
9.80808 

28 
28 
28 
27 
28 

0.  19  303 
0.  19  275 
0.  19  247 
0.  19  219 
0.  19  192 

9.  92  522 
9.  92  514 
9.  92  506 
9.  92  498 
9.92  490 

8 
8 
8 
8 

s 

20 

19 
18 
17 
16 

49  20 
16 
12 
8 
4 

11   0 
4 

8 
12 
16 

45 
46 
47 
48 
49 

9.  73  318 
9.  73  337 
9.73  357 
9.  73  377 
9.  73  396 

19 
20 
20 
19 
20 

9.  80  836 
9.  80  864 
9.  80  892 
9.  80  919 
9.80  947 

28 
28 
27 
28 
28 

0.  19  164 
0.  19  136 
0.  19  108 
0.  19  081 
0.  19  053 

9.  92  482 
9.  92  473 
9.  92  465 
9.  92  457 
9.92  449 

9 

8 
8 
8 

8 

15 
14 
13 
12 
11 

49   0 
56 
52 
48 
44 

11  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  73  416 
9.  73  435 
9.  73  455 
9.  73  474 
9.  73  494 

19 
20 
19 
20 
19 

9.  80  975 
9.81  003 
9.  81  030 
9.81  058 
9.  81  086 

28 
27 
28 
28 
27 

0.19  025 
0.  18  997 
0.  18  970 
0.  18  942 
0.  18  914 

9.  92  441 
9.  92  433 
9.92  425 
9.  92  416 
9.  92  408 

8 
8 
9 
8 
g 

10 

9 

8 
7 
6 

48  40 
36 
32 
28 
24 

11  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  73  513 
9.  73  533 
9.  73  552 
9.  73  572 
9.  73  591 

20 
19 
20 
19 
20 

9.81  113 
9.81  141 
9.  81  169 
9.81  196 
9.81  224 

28 
28 
27 
28 
28 

0.  18  887 
0.  18  859 
0.  18  831 
0.  18  804 
0.  18  776 

9.  92  400 
9.  92  392 
9.92  384 
9.  92  376 
9.  92  367 

8 
8 
8 
9 
8 

5 

4 
3 
2 
1 

48  20 
16 
12 
8 
4 

12   0 

60 

9.  73  611 

9.  81  252 

0.  18  748 

9.  92  359 

0 

48   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

i 

m.  s. 

57° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  181 

TABLE  22.— Five-place  logarithms  of  circular  functions,  etc. — Continued. 

2h  33° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

12   0 
4 
8 
12 
16 

0 

1 

2 
3 
4 

9.  73  611 
9.  73  630 
9.73650 
9.  73  669 
9.  73  689 

19 
20 
19 
20 
1Q 

9.81  252 
9.81  279 
9.81  307 
9.81  335 
9.81  362 

27 
28 
28 
27 

00 

0.  18  748 
0.  18  721 
0.  18  693 
0.  18  665 
0.  18  638 

'  9.  92  359 
9.  92  351 
9.  92  343 
9.  92  335 
9.  92  326 

8 
8 
8 
9 

60 

59 
58 
57 
56 

48   0 
56 
52 
48 
44 

12  20 
24 

28 
32 
36 

5 
6 
7 
8 
9 

9.  73  708 
9.  73  727 
9.  73  747 
9.  73  766 
9.  73  785 

19 
20 
19 
19 

9.81  390 
9.81  418 
9.81  445 
9.81  473 
9.81  500 

28 
27 
28 
27 

0.  18  610 
0.  18  582 
0.18  555 
0.  18  527 
0.  18  500 

9.  92  318 
9.  92  310 
9.  92  302 
9.  92  293 
9.  92  285 

8 
8 
9 
8 

55 
54 
53 
52 
51 

47  40 
36 
32 

28 
24 

12  40 
44 
48 
52 
56 

10 

11 
12 
13 

14 

9.73  805 
9.  73  824 
9.  73  843 
9.73  863 
9.  73  882 

19 
19 
20 
19 

9.81  528 
9.81  556 
9.81  583 
9.  81  611 
9.81  638 

28 
27 
28 
27 

0.  18  472 
0.  18  444 
0.  18  417 
0.  18  389 
0.  18  362 

9.  92  277 
9.  92  269 
9.  92  260 
9.  92  252 

9.  <J2  244 

8 
9 

8 
8 

50 

49 
48 
47 
46 

47  20 
16 
12 

8 
4 

13   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  73  901 
9.  73  921 
9.  73  940 
9.  73  959 
9.  73  978 

20 
19 
19 
19 
1Q 

9.81  666 
9.81  693 
9.81  721 
9.  81  748 
9.81  776 

27 
28 
27 
28 

0.  18  334 
0.  18  307 
0.  18  279 
0.  18  252 
0.  18  224 

9.  92  235 
9.  92  227 
9.  92  219 
9.  92  211 
9.92  202 

8 
8 
8 
9 

45 
44 
43 
42 
41 

47   0 
56 
52 
48 
44 

13  20 
24 
28 
32 
36 

•JO 

21 
22 
23 
24 

9.  73  997 
9.  74  017 
9.  74  036 
9.  74  055 
9.  74  074 

20 
19 
19 
19 
19 

9.81  803 
9.  81  831 
9.81  858 
9.81  886 
9.81  913 

28 
27 
28 
27 

00 

0.  18  197 
0.  18  169 
0.  18  142 
0.  18  114 
0.  18  087 

9.  92  194 
9.  92  186 
9.  92  177 
9.  92  169 
9.  92  161 

8 
9 

8 
8 

<) 

40 

39 
38 
37 
36 

46  40 
36 
32 

28 
24 

13  40 
44 

48 
52 
56 

26 
26 

27 
28 
29 

9.  74  093 
9.74  113 
9.  74  132 
9.74  151 
9.  74  170 

20 
19 
19 
19 
19 

9.81  941 
9.81  968 
9.81  996 
9.82023 
9.  82  051 

27 
28 
27 
28 
27 

0.  18  059 
0.  18  032 
0.  18  004 
0.  17  977 
0.  17  949 

9.  92  152 
9.  92  144 
9.  92  136 
9.  92  127 
9.  92  119 

8 
8 
9 

8 

g 

35 
34 
33 
32 
31 

46  20 
16 

12 
8 
4 

14   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  74  189 
9.  74  208 
9.  74  227 
9.  74  246 
9.  74  265 

19 
19 
19 
19 
19 

9.  82  078 
9.  82  106 
9.82  133 
9.82  161 
9.82  188 

28 
27 
28 
27 

0.  17  922 
0.  17  894 
0.  17  867 
0.  17  839 
0.  17  812 

9.  92  111 
9.92  102 
9.92  094 
9.  92  086 
9.  92  077 

9 
8 
8 
9 

80 

29 
28 
27 
26 

46   0 
56 
52 
48 
44 

14  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.74  284 
9.  74  303 
9.  74  322 
9.  74  341 
9.74  360 

19 
19 
19 
19 
19 

9.  82  215 
9.  82  243 
9.82  270 
9.  82  298 
9.82  325 

28 
27 
28 
.  27 
27 

0.  17  785 
0.  17  757 
0.  17  730 
0.  17  702 
0.  17  675 

9.  92  069 
9.  92  060 
9.  92  052 
9.  92  044 
9.  92  035 

9 

8 
8 
9 

g 

25 
24 
23 
22 
21 

45  40 
36 
32 
28 
24 

14  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  74  379 
9.74  398 
9.  74  417 
9.  74  436 
9.  74  455 

19 
19 
19 
19 
19 

9.82  352 
9.82  380 
9.  82  407 
9.82  435 
9.  82  462 

2S 
27 
28 
27 
97 

0.  17  648 
0.  17  620 
0.  17  59? 
0.17  565 
0.  17  538 

9.  92  027 
9.  92  018 
9.  92  010 
9.  92  002 
9.91  993 

9 

8 
8 
9 

20 

19 
18 
17 
16 

45  20 
16 
J2 
8 
4 

15   0 

4 
8 
12 
16 

45 
46 
47 

48 
49 

9.  74  474 
9.  74  493 
9.  74  512 
9.  74  531 
9.  74  549 

19 
19 
19 
18 
19 

9.  82  489 
9.  82  517 
9.  82  544 
9.  82  571 
9.  82  599 

28 
27 
27 

28 

27 

0.  17  511 
0.  17  483 
0.  17  456 
0.  17  429 
0.  17  401 

9.91  985 
9.91  976 
9.91  968 
9.91  959 
9.91  951 

9 
8 
9 
8 
9 

15 
14 
13 
12 
11 

45   0 
56 
52 

48 
44 

1&  20 

24 
28 
32 
36 

50 

51 
52 
53 
54 

9.74.568 
9.  74  587 
9.  74  606 
9.  74  625 
9.74  644 

19 
19 
19 
19 

18 

9.82  626 
9.82  653 
9.82  681 
9.82  708 
9.  82  735 

27 
28 
27 
27 
27 

0.  17  374 
0.  17  347 
0.  17  319 
0.  17  292 
0.  17  265 

9.  91  942 
9.  91  934 
9.91  925 
9.91  917 
9.91  908 

8 
9 
8 
9 

g 

10 

9 

8 
7 
6 

44  40 
36 
32 
28 
24 

15  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  74  662 
9.  74  681 
9.  74  700 
9.  74  719 
9.  74  737 

19 
19 
19 
18 
19 

9.82  762 
9.82  790 
9.  82  817 
9.  82  844 
9.  82  871 

28 
27 
27 
27 
28 

0.  17  238 
0.  17  210 
0.  17  183 
0.  17  156 
0.17  129 

9.91  900 
9.  91  891 
9.91  883 
9.  91  874 
9.91  866 

9 
8 
9 
8 
9 

5 
4 
3 

2 
1 

44  20 
16 
12 

8 

1 

16   0 

60 

9.  74  756 

9.  82  899 

0.  17  101 

9.  91  857 

0 

44   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

58° 


182  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  34° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

16   0 
4 
8 
12 
16 

0 

1 
2 

3 
4 

9.  74  756 
9.  74  775 
9.74  794 
9.  74  812 
9.  74  831 

19 
19 
18 
19 
19 

9.  82  899 
9.82  926 
9.82  953 
9.  82  980 
9.83  008 

27 
27 
27 
28 
27 

0.  17  101 

0.  17  074 
0.  17  047 
0.  17  020 
0.  16  992 

9.  91  857 
9.  91  849 
9.  91  840 
9.  91  832 
9.91  823 

8 
9 
8 
9 

60 

59 
58 
57 
56 

44   0 

56 
52 
48 
44 

16  20 
24 

28 
32 
36 

5 

' 

8 
9 

9.  74  850 
9.  74  868 
9.  74  887 
9.  74  906 
9.  74  924 

18 
19 
19 
18 
19 

9.83  035 
9.83  062 
9.  83  089 
9.83  117 
9.83  144 

27 
27 
28 
27 
27 

0.16  965 
0.  16  938 
0.  16  911 
0.  16  883 
0.  16  856 

9.91  815 
9.  91  806 
9.91  798 
9.  91  789 
9.91  781 

9 
8 
9 
8 
g 

55 
54 
53 
52 
51 

43  40 
36 
32 

28 
24 

16  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  74  943 
9.  74  961 
9.  74  980 
9.  74  999 
9.  75  017 

18 
19 
19 
18 
19 

9.  83  171 
9.83  198 
9.  83  225 
9.  83  252 
9.  83  280 

27 
27 
27 
28 
27 

0.  16  829 
0.  16  802 
0.  16  775 
0.  16  748 
0.  16  720 

9.  91  772 
9.91  763 
9.91  755 
9.  91  746 
9.  91  738 

9 

8 
9 
8 
g 

50 

49 
48 
47 
46 

43  20 
16 
12 
8 
4 

17   0 
4 

8 
12 
16 

15 

16 
17 
18 
19 

9.  75  036 
9.  75  054 
9.  75  073 
9.  75  091 
9.  75  110 

18 
19 
18 
19 

18 

9.  83.  307 
9.  83  334 
9.  83  361 
9.83  388 
9.  83  415 

27 
27 
27 
27 
27 

0.  16  693 
0.  16  666 
0.  16  639 
0.16612 
0.  16  585 

9.91  729 
9.91  720 
9.91  712 
9.  91  703 
9.  91  695 

9 

8 
9 
8 
9 

45 
44 
43 
42 
41 

43   0 

56 
52 
48 
44 

17  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  75  128 
9.  75  147 
9.  75  165 
9.  75  184 
9.  75  202 

19 

18 
19 
18 
19 

9.  83  442 
9.  83  470 
9.83  497 
9.83  524 
9.  83  551 

28 
27 
27 
27 

27 

0.  16  558 
0.  16  530 
0.  16  503 
0.  16  476 
0.  16  449 

9.91  686 
9.91  677 
9.  91  669 
9.  91  660 
9.91  651 

9 

8 
9 
9 

8 

40 

39 
38 
37 
36 

42  40 
36 
32 

28 
24 

17  40 
44 

48 
52 
56 

25 
26 

27 
28 
29 

9.  75  221 
9.  75  239 
9.  75  258 
9.  75  276 
9.  75  294 

18 
19 
18 
18 
19 

9.  83  578 
9.  83  605 
9.  83  632 
9.83  659 
9.  83  686 

27 
27 
27 
27 
27 

0.  16  422 
0.  16  395 
0.  16  368 
0.  16  341 
0.  16  314 

9.91  643 
9.91  534 
9.91  625 
9.91  617 
9.91  608 

9 
9 
8 
9 
9 

35 
34 
33 
32 
31 

42  20 
16 
12 
8 
4 

18   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  75  313 
9.  75  331 
9.  75  350 
9.  75  368 
9.  75  386 

•  18 
19 
18 
18 
19 

9.  83  713 
9.  83  740 
9.  83  768 
9.  83  795 
9.83  822 

27 
28 
27 
27 
07 

0.  16  287 
0.  16  260 
0.  16  232 
0.  16  205 
0.  16  178 

9.91  599 
9.91  591 
9.  91  582 
9.91  573 
9.  91  565 

8 
9 
9 
8 
9 

30 

29 
28 
27 
26 

42   0 

56 
52 
48 
44 

18  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  75  405 
9.  75  423 
9.  75  441 
9.  75  459 
9.  75  478 

18 
18 
18 
19 
18 

9.  83  849 
9.83876 
9.  83  903 
9.  83  930 
9.  83  957 

27 

27 
27 

27 
27 

0.  16  151 
0.  16  124 
0.  16  097 
0.  16  070 
0.  16  043 

9.91  556 
9.91  547 
9.91  538 
9.91  530 
9.  91  521 

9 
9 
8 
9 
9 

25 
24 
23 
22 
21 

41  40 
36 
32 
28 
24 

18  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  75  496 
9.  75  514 
9.  75  533 
9.  75  551 
9.  75  569 

18 
-19 
18 
18 
18 

9.  83  984 
9.  84  Oil 
9.84  038 
9.84  065 
9.  84  092 

27 
27 
27 

27 
97 

0.  16  016 
0.  15  989 
0.  15  962 

Oi  15  908 

9.  91  512 
9.91  504 
9.91  495 
9.  91  486 
9.91  477 

8 
9 
9 
9 

g 

20 

19 
18 
17 
16 

41  20 
16 
12 
8 
4 

19   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.  76  587 
9.  75  605 
9.  75  624 
9.  75  642 
9.75  660 

18 
19 
18 
18 
18 

9.84  119 
9.84  146 
9.84  173 
9.  84  200 
9.84  227 

27 
27 

27 
27 
27 

0.  15  881 
0.  15  854 
0.  15  827 
0.  15  800 
0.  15  773 

9.91  469 
9.91  460 
9.91  451 
9.91  442 
9.  91  433 

9 
9 
9 
9 

8 

15 
14 
13 
12 
11 

41   0 

56 
52 
48 
44 

19  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  75  678 
9.  75  696 
9.  75  714 
9.  75  733 
9.  75  751 

18 
18 
19 
18 
18 

9.84  254 
9.  84  280 
9.84  307 
9.84  334 
9.  84  361 

26 
27 
27 
27 
27 

0.  15  746 
0.  15  720 
0.  15  693 
0.  15  666 
0.  15  639 

9.91  425' 
9.  91  416 
9.91  407 
9.91  398 
9.91  389 

9 
9 
9 
9 

g 

10 

9 

8 
7 
6 

40  40 
36 
32 
28 
24 

19  40 
44 

48 
52 
56 

55 
56 
57 

58 
59 

9.  75  769 
9.  75  787 
9.  75  805 
9.  75  823 
9.  75  841 

18 
18 
18 
18 
18 

9.84  388 
9.84  415 
9.84  442 
9.84  469 
9.  84  496 

27 
27 
27 
27 
27 

0.  15  612 
0.  15  585 
0.  15  558 
0.  15  531 
0.15  504 

9.  91  381 
9.91  372 
9.91  363 
9.91  354 
9.91  345 

9 
9 
9 
9 
9 

5 
4 
3 

2 
1 

40  20 
16 
12 
8 
4 

20   0 

60 

9.  75  859 

9.  84  523 

0.  15  477 

9.91  336 

0 

40   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

m.  s. 

55° 


GEOGRAPHIC  '  TABLES  AND  FORMULAS.  183 

• 
TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

2h  35° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

20   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  75  859 
9.  75  877 
9.  75  895 
9.  75  913 
9.  75  931 

18 
18 
18 
18 

9.84  523 
9.84  550 
9.  84  576 
9.84  603 
9.84630 

27 
26 
27 
27 
97 

0.  15  477 
0.  15  450 
0.  15  424 
0.  15  397 
0.  15  370 

9.91  336 
9.  91  328 
9.91  319 
9.  91  310 
9.91  301 

8 
9 
9 
9 

60 

59 
58 
57 
56 

40   0 
56 
52 
48 
44 

20  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  75  949 
9.  75  967 
9.  75  985 
9.  76  003 
9.  76  021 

18 
18 
18 
18 

10 

9.84  657 
9.84  684 
9.84711 
9.84  738 
9.84764 

27 
27 
27 
26 
07 

0.  15  343 
0.  15  316 
0.  15  289 
0.  15  262 
0.  15  236 

9.  91  292 
9.91  283 
9.91  274 
9.91  266 
9.91  257 

9 
9 

8 
9 

ii 

55 
54 
53 
52 
51 

39  40 
36 
32 

28 
24 

20  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  76  039 
9.  76  057 
9.  76  075 
9.  76  093 
9.76  111 

18 
18 
18 
18 
IS 

9.  84  791 
9.84  818 
9.84  845 
9.  84  872 
9.84  899 

27 
27 
27 
27 

nc 

0.  15  209 
0.  15  182 
0.  15  155 
0.  15  128 
0.15101 

9.91  248 
9.91  239 
9.91  230 
9.  91  221 
9.91  212 

9 
9 
9 
9 

<i 

50 

49 
48 
47 
46 

39  20 
16 
12 
8 
4 

21   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.76  129 
9.  76  146 
9.  76  164 
9.  76  182 
9.  76  200 

17 
18 
18 
18 

9.  84  925 
9.84  952 
9.  84  979 
9.85006 
9.  85  033 

27 
27 
27 
27 

0.  15  075 
0.  15  048 
0.15021 
0.  14  994 
0.  14  967 

•  9.  91  203 
9.  91  194 
9.  91  185 
9.91  176 
9.91  167 

9 
9 
9 
9 

45 
44 
43 
42 
41 

39   0 
56 
52 
48 
44 

21  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  76  218 
9.  76  236 
9.  76  253 
9.76  271 
9.  76  289 

18 
17 
18 
18 

9.  85  059 
9.  85  086 
9.85  113 
9.85  140 
9.85  166 

27 
27 
27 
26 

0.  14  941 
0.  14  914 
0.  14  887 
0.  14  860 
0.  14  834 

9.91  158 
9.91  149 
9.91  141 
9.  91  132 
9.  91  123 

9 
8 
9 
9 

40 

39 
38 
37 
36 

38  40 
36 
32 
28 
24 

21  40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

9.  76  307 
9.  76  324 
9.  76  342 
9.76  360 
9.  76  378 

17 
18 
18 
18 

9.  85  193 
9.85220 
9.  85  247 
9.85273 
9.85  300 

27 
27 
26 
27 

0.  14  807 
0.  14  780 
0.  14  753 
0.  14  727 
0.  14  700 

9.91  114 
9.  91  105 
9.91  096 
9.91  087 
9.  91  078 

9 
9 
9 
9 
9 

35 
34 
33 
32 
31 

38  20 
16 
12 
8 
4 

22   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  76  395 
9.  76  413 
9.  76  431 
9.  76  448 
9.  76  466 

18 
18 
17 
18 

-10 

9.  85  327 
9.85  354 
9.85  380 
9.85  407 
9.85434 

27 
26 
27 
27 

0.  14  673 
0.  14  646 
0.  14  620 
0.  14  593 
0.  14  566 

9.91  069 
9.  91  060 
9.91  051 
9.  91  042 
9.91  033 

9 

9 
9 
9 
10 

30 

29 
28 
27 
26 

38   0 
56 
52 
48 
44 

•1-1  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.76  884 
9.  76  501 
9.  76  519 
9.  76  537 
9.76  554 

17 
18 
18 
17 
18 

9.85460 
9.  85  487 
9.85  514 
9.85  540 
9.  85  567 

27 
27 
26 
27 

0.14  540 
0.  14  513 
0.  14  486 
0.  14  460 
0.  14  433 

9.  91  023 
9.91  014 
9.  91  005 
9.  90  996 
9.  90  987 

9 

9 
9 
9 
9 

25 
24 
23 
22 
21 

37  40 
36 
32 
28 
24 

22  40 
44 
•  48 
52 
56 

40 

41 
42 
43 
44 

9.  76  572 
9.76  590 
9.  76  607 
9.  76  625 
9.  76  642 

18 
17 
18 
17 

9.  85  594 
9.  85  620 
9.  85  647 
9.85  674 
9.  85  700 

26 
27 
27 
26 

0.  14  406 
0.14  380 
0.  14  353 
0.  14  326 
0.14  300 

9.  90  978 
9.  90  969 
9.  90  960 
9.  90  951 
9.  90  942 

9 

9 
9 
9 
9 

20 

19 
18 
17 
16 

37  20 
16 
12 
8 
4 

23   0 
4 
8 
12 
16 

45 

46 
47 
48 
49 

9.76  660 
9.  76  677 
9.  76  695 
9.  76  712 
9.  76  730 

17 
18 
17 
18 

9.85  727 
9:85  754 
9.85  780 
9.85  807 
9.85834 

27 
?6 

27 
27 

0.  14  273 
0.  14  246 
0.  14  220 
0.  14  193 
0.  14  166 

9.90933 
9.  90  924 
9.  90  915 
9.90  906 
9.  90  896 

9 
9 
9 
10 
9 

15 
14 
13 
12 
11 

37   0 
56 
52 

48 
44 

23  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  76  747 
9.  76  765 
9.  76  782 
9.76800 
9.  76  817 

18 
17 
18 
17 

-IQ 

9.85  860 
9.85  887 
9.85  913 
9.85  940 
9.  85  967 

27 
26 
27 
27 

0.  14  140 
0.  14  113 
0.  14  087 
0.  14  060 
0.  14  033 

9.90  887 
9.  90  878 
9.  90  869 
9.90860 
9.  90  851 

9 
9 
9 
9 
9 

10 

9 
8 
7 
6 

36  40 
36 
32 

28 
24 

23  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.76  835 
9.  76  852 
9.  76  870 
9.  76  887 
9.76904 

17 
18 
17 
17 

9.  85  993 
9.86  020 
9.  86  046 
9.  86  073 
9.86  100 

27 
26 
27 
27 

0.  14  007 
0.  13  980 
0.  13  954 
0.13  927 
0.13  900 

9.90  842 
9.90832 
9.  90  823 
9.  90  814 
9.90805 

10 
9 
9 
9 
9 

5 

4 
3 
2 
1 

36  20 
16 
12 
8 
4 

24   0 

60 

9.76  922 

9.  86  126 

0.  13  874 

9.  90  796 

0 

36   0 

L.Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

i 

m.  s. 

54° 


184  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

2h  36° 


m.  s. 

r 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

24  0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  76  922 
9.  76  939 
9.  76  957 
9.  76  974 
9.  76  991 

17 
18 
17 
17 
18 

9.  86  126 
9.  86  153 
9.  86  179 
9.  86  206 
9.  86  232 

27 
26 
27 
26 

27 

0.  13  874 
0.  13  847 
0.  13  821 
0.  13  794 
0.  13  768 

9.  90  796 
9.  90  787 
9.  90  777 
9.  90  768 
9.  90  759 

9 
10 
9 
9 
9 

60 

59 
58 
57 
56 

36   0 
56 

52 
48 
44 

24  20 
24 
28' 
32 
36 

5 
6 

7 
8 
9 

9.  77  009 
9.  77  026 
9.  77  043 
9.  77  061 
9.  77  078 

17 
17 
18 
17 
17 

9.  86  259 
9.  86  285 
9.  86  312 
9.  86  338 
9.  86  365 

26 
27 
26 

27 

27 

0.  13  741 
0.  13  715 
0.  13  688 
0.  13  662 
0.  13  635 

9.  90  750 
9.  90  741 
9.  90  731 
9.  90  722 
9.90  713 

9 
10 
9 
9 
9 

55 
54 
53 
52 
51 

35  40 
36 
32 

28 
24 

24  40 
44 
48 
52 
56 

10 

11 
12 

13 
14 

9.  77  095 
9.  77  112 
9.  77  130 
9.  77  147 
9.  77  164 

17 
18 
17 
17 
17 

9.  86  392 
9.  86  418 
9.  86  445 
9.  86  471 
9.  86  498 

26 
27 
26 
27 
26 

0.  13  608 
0.  13  582 
0.  13  555 
0.  13  529 
0.  13  502 

9.  90  704 
9.  90  694 
9.90685 
9.  90  676 
9.  90  667 

10 
9 
9 
9 
10 

50 

49 

48 
47 
46 

35  20 
16 

12 

8 
4 

25   0 

4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  77  181 
9.77  199 
9.  77  216 
9.  77  233 
9.  77  250 

18 
17 
17 
17 
18 

9.  86  524 
9.  86  551 
9.  86  577 
9.86  603 
9.  86  630 

27 
26 
26 
27 
26 

0.  13  476 
0.  13  449 
0.  13  423 
0.  13  397 
0.  13  370 

9.  90  657 
9.  90  648 
9.  90  639 
9.  90  630 
9.  90  620 

9 
9 
9 
10 
9 

45 
44 
43 
42 
41 

35   0 
56 
52 
48 
44 

25  20 
24 

28 
32 
36 

20 

21 
22 
23 
24 

9.  77  268 
9.  77  285 
9.  77  302 
9.  77  319 
9.  77  336 

17 
17 
17 
17 
17 

9.  86  656 
9.  86  683 
9.  86  709 
9.  86  736 
9.  86  762 

27 
26 
27 
26 
27 

0.  13  344 

0.  13  317 
0.13  291 
0.  13  264 
0.  13  238 

9.  90  611 
9.  90  602 
9.90  592 
9.  90  583 
9.90574 

9 
10 
9 
9 
9 

40 

39 
38 
37 
36 

34  40 
36 
32 
28 
24 

25  40 
44 
48 
52 
56 

25 
26 

27 
28 
29 

9.  77  353 
9.  77  370 
9.  77  387 
9.  77  405 
9.  77  422 

17 
17 
18 
17 
17 

9.86  789 
9.86  815 
9.  86  842 
9.  86  868 
9.  86  894 

26 
27 
26 
26 
27 

0.  13  211 
0.  13  185 
0.  13  158 
0.13  132 
0.  13  106 

9.90  56$ 
9.  90  555 
9.  90  546 
9.  90  537 
9.  90  527 

10 
9 
9 
10 
9 

35 
34 
33 
32 
31 

34  20 
16 
12 
8 
4 

26   0 
4 

8 
12 
16 

30 

31 
32 
33 
34 

9.  77  439 
9.  77  456 
9.  77  473 
9.  77  490 
9.  77  507 

17 
17 
17 
17 
17 

9.  86  921 
9.  86  947 
9.  86  974 
9.  87  000 
9.87  027 

26 
27 
26 
27 
26 

0.  13  079 
0.  13  053 
0.  13  026 
0.13  000 
0.  12  973 

9.  90  518 
9.  90  509 
9.  90  499 
9.  90  490 
9.  90  480 

9 
10 
9 
10 
9 

80 

29 

28 
27 
26 

34   0 

56 
52 
48 
44 

26  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  77  524 
9.  77  541 
9.  77  558 
9.  77  575 
9.  77  592 

17 
17 
17 
17 
17 

9.  87  053 
9.  87  079 
9.  87  106 
9.  87  132 
9.  87  158 

26 
27 
26 
26 
27 

0.  12  947 
0.12  921 
0.  12  894 
0.  12  868 
0.  12  842 

9.  90  471 
9.  90  462 
9.  90  442 
9.  90  443 
9.  90  434 

9 
10 
9 
9 
10 

25 
24 
23 
22 
21 

33  40 
36 
32 

28 
24 

26  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.  77  609 
9.  77  626 
9.  77  643 
9.  77  660 
9.  77  677 

17 
17 
17 
17 

17 

9.87  185 
9.  87  211 
9.  87  238 
9.  87  264 
9.  87  290 

26 
27 
26 
26 
27 

0.  12  815 
0.  12  789 
0.  12  762 
0.  12  736 
0.  12  710 

9.  90  424 
9.  90  415 
9.  90  405 
9.  90  396 
9.  90  386 

9 
10 
9 
10 
9 

20 

19 
18 
17 
16 

33  20 
16 
12 
8 
4 

27   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.  77  694 
9.  77  711 
9.  77  728 
9.  77  744 
9.  77  761 

17 
17 
16 
17 
17 

9.  87  317 
9.87  343 
9.87  369 
9.  87  396 
9.  87  422 

26 
26 
27 
26 
26 

0.  12  683 
0.  12  657 
0.  12  631 
0.  12  604 
0.  12  578 

9.  90  377 
9.  90  368 
9.90  358 
9.  90  349 
9.  90  339 

9 
10 
9 
10 
9 

15 
14 
13 
12 
11 

33   0 

56 
52 
48 
44 

27  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  77  778 
9.  77  795 
9.  77  812 
9.  77  829 
9.  77  846 

17 
17 
17 
17 
16 

9.  87  44X 
9.  87  475 
9.87  501 
9.  87  527 
9.  87  554 

27 
26 
26 
27 
26 

0.  12  552 
0.  12  525 
0.  12  499 
0.  12  473 
0.  12  446 

9.  90  330 
9.  90  320 
9.  90  311 
9.  90  301 
9.  90  292 

10 
9 
10 
9 
10 

10 

9 

8 

7 
6 

32  40 
36 
32 

28 
24 

27  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  77  862 
9.  77  879 
9.  77  896 
9.  77  913 
9.  77  930 

17 
17 
17 
17 
16 

9.  87  680 
9.  87  606 
9.  87  633 
9.87  65§ 
9.  87  685 

26 
27 
26 
26 
26 

0.  12  420 
0.  12  394 
0.  12  367 
0.  12  341 
0.  12  315 

9.  90  282 
9.  90  273 
9.  90  263 
9.  90  254 
9.  90  244 

9 
10 
9 
10 
9 

5 
4 
3 
2 
1 

32  20 
16 
12 
8 
4 

28   0 

60 

9.  77  946 

9.  87  711 

0.  12  289 

9.90  235 

0 

32   0 

L.  Co*. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

53° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  185 

TABLE  22. — Five-place  logarithms  of  circular  functions,  ete. — Continued. 
2h  370 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

28   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  77  946 
9.  77  963 
9.77  980 
9.  77  997 
9.  78  013 

17 
17 
17 
16 
17 

17 
16 
17 
17 
16 

17 
17 
16 
17 
17 

16 
17 
16 
17 
17 

16 
17 
16 
17 
16 

17 
16 
17 
16 
17 

16 
17 
16 
16 
17 

16 
17 
16 
16 
17 

16 
17 
16 
16 
17 

9.  87  711 
9.  87  738 
9.  87  764 
9.87  790 
9.87  817 

27 
26 
26 
27 
26 

26 
26 
27 
26 
26 

26 
27 
26 
26 
26 

26 
27 
26 
26 
26 

26 
27 
26 
26 
26 

26 
27 
26 
26 

26 

26 
26 
27 
26 
26 

26 
26 
26 
26 
26 

27 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
27 
26 
26 
26 

26 
26 
26 
26 
26 

0.  12  289 
0.  12  262 
0.  12  236 
0.  12  210 
0.  12  183 

9.90  235 
9.90  225 
9.  90  216 
9.  90  206 
9.  90  197 

10 
9 
10 
9 
10 

60 

54 
58 
57 
56 

32   0 
56 
52 
48 
44 

28  20 
24 
28 
32 
36 

5 
6 

7 
8 
9 

9.  78  030 
9.  78  047 
9.78  063 
9.78  080 
9.  78  097 

9.87  843 
9.  87  869 
9.  87  895 
9.87  922 
9.  87  948 

0.  12  157 
0.  12  131 
0.  12  105 
0.  12  078 
0.  12  052 

9.  90  187 
9.  90  178 
9.90  168 
9.  90  159 
9.  90  149 

9 
10 
9 
10 
10 

55 
54 
53 
52 
51 

31  40 
36 
32 
28 
24 

28  40 
44 
48 
52 
66 

10 

11 
12 
13 
14 

9.78  113 
9.  78  130 
9.  78  147 
9.  78  163 
9.  78  180 

9.  87  974 
9.88000 
9.  88  027 
9.88  053 
9.  88  079 

0.  12  026 
0.12  000 
0.  11  973 
0.11  947 
0.  11  921 

9.90  139 
9.90  130 
9.90  120 
9.90  111 
9.  90  101 

9 
10 
9 
10 
10 

9 
10 
9 
10 
10 

9 
10 
10 
9 
10 

10 
9 
10 
10 
9 

10 
10 
9 
10 
10 

10 
9 
10 
10 
10 

9 
10 
10 
10 
9 

10 
10 
10 
10 
9 

10 
10 
10 
10 
10 

9 
10 
10 
10 
10 

50 

49 
48 
47 
46 

31  20 
16 
12 
8 
4 

29   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  78  197 
9.  78  213 
9.78  230 
9.78  24C 
9.  78  263 

9.88  105 
9.  88  131 
9.88  158 
9.88  184 
9.88210 

0.  11  895 
0.  11  869 
0.  11  842 
0.  11  816 
0.  11  790 

9.90  091 
9.  90  082 
9.  90  072 
9.90063 
9.90  053 

45 
44 
43 
42 
41 

31   0 

56 
52 
48 
44 

29  20 
24 
28 
32 
36 

20 

21 

22 
23 
24 

9.78  280 
9.  78  296 
9.  78  313 
9.  78  329 
9.  78  346 

9.88236 
9.  88  262 
9.88  289 
9.  88  315 
9.88  841 

0.11  764 
0.  11  738 
0.  11  711 
0.11  685 
0.  11  659 

9.90  043 
9.  90  034 
9.  90  024 
9.  90  014 
9.90  005 

40 

39 
38 
37 
36 

30  40 
36 
32 
28 
24 

29  40 
44 
48 
52 
56 

25 
26 
27 

28 
29 

9.  78  362 
9.  78  379 
9.  78  395 
9.  78  412 
9.78  428 

9.88367 
9.  88  393 
9.  88  420 
9.  88  446 
9.  88  472 

0.11  633 
0.  11  607 
0.  11  580 
0.  11  554 
0.  11  528 

9.  89  995 
9.89985 
9.  89  976 
9.  89  966 
9.  89  956 

35 
34 
33 
32 
31 

30  20 
•   16 
12 
8 
4 

30   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

«J.  7.S  4-45 
9.  78  461 
9.  78  478 
9.  78  494 
9.  78  510 

9.  88  498 
9.  88  524 
9.88  550 
9.  88  577 
9.88  603 

0.11  502 
0.  11  476 
0.11  450 
0.11  423 
0.  11  397 

9.  89  947 
9.  89  937 
9.89  927 
9.  89  918 
9.  89  908 

80 

29 
28 
27 
26 

30   0 
56 
52 

48 
44 

30  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  78  527 
9.  78  543 
9.  78  560 
9.  78  576 
9.  78  592 

9.88  629 
9.88  655 
9.  88  681 
9.88  707 
9.88  733 

0.  11  371 
0.11  345 
0.  11  319 
0.  11  293 
0.  11  267 

9.89898 
9.  89  888 
9.  89  879 
9.  89  869 
9.  89  859 

25 
24 
23 
22 
21 

29  40 
36 
32 
28 
24 

30  40 
44 
48 
62 
66 

40 

41 
42 
43 
44 

9.  78  609 
9.  78  625 
9.78  642 
9.  78  658 
9.  78  674 

9.  88  759 
9.  88  786 
9.  88  812 
9.  88  838 
9.88864 

0.  11  241 
0.  11  214 
0.  11  188 
0.  11  162 
0.  11  136 

9.  89  849 
9.89840 
9.89  830 
9.89  820 
9.  89  810 

20 

19 
18 
17 
16 

29  20 
16 
12 

8 
4 

31   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

9.  78  691 
9.  78  707 
9.  78  723 
9.  78  739 
9.  78  756 

16 
16 
16 
17 
16 

16 
17 
16 
16 
16 

16 
17 
16 
16 
16 

9.88  890 
9.  88  916 
9.  88  942 
9.  88  968 
9.  88  994 

0.11  110 
0.  11  084 
0.  11  068 
0.  11  032 
0.  11  006 

9.  89  801 
9.  89  791 
9.  89  781 
9.  89  771 
9.89  761 

15 
14 
13 
12 
11 

29   0 
66 
52 
48 
44 

31  20 
24 
28 
32 
36 

50 

61 
52 
53 
54 

9.  78  772 
9.  78  788 
9.78  805 
9.  78  821 
9.  78  837 

9.89  020 
9.  89  046 
9.  89  073 
9.89  099 
9.  89  125 

0.  10  980 
0.  10  954 
0.  10  927 
0.  10  901 
0.  10  875 

9.897f.2 
9.  89  742 
9.  89  732 
9.  89  722 
9.  89  712 

10 

9 

8 
7 
6 

28  40 
36 
32 
28 
24 

31  40 
44 

48 
52 
56 

55 
56 
57 
58 
59 

9.78853 
9.  78  869 
9.78  886 
9.78902 
9.78  918 

9.  89  151 
9.89  177 
9.  89  203 
9.  89  229 
9.  89  255 

0.  10  849 
0.  10  823 
0.  10  797 
0.  10  771 
0.  10  745 

9.  89  702 
9.  89  693 
9.  89  683 
9.  89  673 
9.89  663 

5 
4 
3 
2 
1 

28  20 
16 
12 
8 
4 

32   0 

60 

9.78  934 

9.89281 

0.  10  719 

9.89  663 

0 

28   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

52° 


186  GEOGRAPHIC  TABLES  AND  FOEMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

2h  38° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

32   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  78  934 
9.  78  950 
9.78  967 
9.  78  983 
9.  78  999 

16 
17 
16 
16 

9.  89  281 
9.  89  307 
9.  89  333 
9.  89  359 
9.  89  385 

26 
26 
26 
26 

0.  10  719 
0.  10  693 
0.  10  667 
0.  10  641 
0.  10  615 

9.89  653 
9.  89  643 
9.  89  633 
9.89  624 
9.  89  614 

10 
10 
9 
10 

60 

59 
58 
57 
56 

28   0 
56 
52 
48 
44 

32  20 

24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  79  015 
9.  79  031 
9.  79  047 
9.  79  063 
9.  79  079 

16 
16 
16 
16 

9.89  411 
9.  89  437 
9.  89  463 
9.89  489 
9.  89  515 

26 
26 
26 
26 

0.  10  589 
0.  10  563 
0:  10  537 
0.  10  511 

0.  10  485 

9.  89  604 
9.  89  594 
9.  89  584 
9.  89  574 
9.  89  564 

10 
10 
10 
10 

55 
54 
53 
52 
51 

27  40 
36 
32 
28 
24 

32  40 
44 
48 
52 
56 

10 

11 
12 
13 

14 

9.  79  095 
9.  79  111 
9.79  128 
9.  79  144 
9.  79  160 

16 
17 
16 
16 

9.  89  541 
9.89  567 
9.  89  593 
9.89  619 
9.  89  645 

26 
26 
26 

26 

0.  10  459 
0.  10  433 
0.  10  407 
0.  10  381 
0.  10  355 

9.89554 
9.  89  544 
9.89  534 
9.89  524 
9.89  514 

10 
10 
10 
10 

50 

49 
48 
47 
46 

27  20 
16 
12 

8 
4 

33   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  79  176 
9.  79  192 
9.  79  208 
9.  79  224 
9.  79  240 

16 
16 
16 
16 

9.  89  671 
9.89  697 
9.  89  723 
9.  89  749 
9.  89  775 

26 
26 
26 
26 

0.  10  329 
0.  10  303 
0.  10  277 
0.  10  251 
0.  10  225 

9.  89  504 
9.  89  495 
9.  89  485 
9.  89  475 
9.  89  465 

.  9 
10 
10 
10 

45 
44 
43 
42 

41 

27   0 
56 
52 
48 
44 

33  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  79  256 
9.  79  272 
9.  79  288 
9.  79  304 
9.  79  319 

16 
16 
16 
15 

9.  89  801 
9.  89  827 
9.  89  853 
9.  89  879 
9.89  905 

26 
26 
26 
26 

0.  10  199 
0.  10  173 
0.  10  147 
0.  10  121 
0.  10  095 

9.  89  455 
9.  89  445 
9.  89  435 
9.  89  425 
9.  89  415 

10 

10 
10 
10 
10 

40 

39 
38 
37 
36 

26  40 
36 
32 

28 
24 

33  40 
44 

48 
52 
56 

25 
26 
27 
28 
29 

9.  79  335 
9.  79  351 
9.  79  367 
9.  79  383 
9.  79  399 

16 
16 
16 
16 

9.89  931 
9.  89  957 
9.  89  983 
9.90009 
9.  90  035 

26 
26 
26 
26 

0.  10  069 
0.  10  043 
0.10  017 
0.  09  991 
0.  09  965 

9.  89  405 
9.  89  395 
9.89  385 
9.89  375 
9.  89  364 

10 
10 
10 

11 

35 
34 
33 
32 
31 

26  20 
16 
12 
8 
4 

34   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  79  415 
9.  79  431 
9.  79  447 
9.  79  463 
9.  79  478 

16 
16 
16 
15 

9.  90  061 
9.  90  086 
9.  90  112 
9.90  138 
9.  90  164 

25 
26 
26 
26 

0.  09  939 
0.09  914 
0.  09  888 
0.  09  862 
0.  09  836 

9.89  354 
9.  89  344 
9.  89  334 
9.  89  324 
9.89  314 

10 
10 
10 
10 

30 

29 
28 
27 
26 

26   0 

56 
52 
48 
44 

34  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  79  494 
9.  79  510 
9.  79  526 
9.  79  542 
9.  79  558 

16 
16 
16 
16 

9.90  190 
9.  90  216 
9.  90  242 
9.  90  268 
9.  90  294 

26 
26 
26 
26 

0.  09  810 
0.09  784 
0.09  758 
0.09  732 
0.09  706 

9.  89  304 
9.  89  294  „ 
9.  89  284 
9.89  274 
9.  89  264 

1Q 
10 
10 
10 

25 
24 
23 
22 

21 

25  40 
36 
32 
28 
24 

34  40 
44 

48 
52 
56 

40 

41 
42 
'43 
44 

9.  79  573 

n  nn  FxQQ 

9!  79  605 
9.  79  621 
9.  79  636 

16 
16 
16 
15 

9.  90  320 
9.  90  346 
9.  90  371 
9.90  397 
9.  90  423 

26 
25 
26 
26 

0.  09  680 
0.  09  654 
0.  09  629 
0.  09  603 
0.  09  577 

9.  89  254 
9.  89  244 
9-.  89  233 
9.  89  223 
9.  89  213 

10 

11 

10 
10 

20 

19 
18 
17 
16 

25  20 
16 
12 

8 
4 

35   0 

4 
8 
12 
16 

45 
46 
47 
48 
49 

.9.  79  652 
9.  79  668 
9.  79  684 
9.  79  699 
9.  79  715 

16 
16 
_15 
16 

9.  90  449 
9.  90  475 
9.90  501 
9.  90  527 
9.  90  553 

26 
26 
26 
26 

0.  09  551 
0.  09  525 
0.  09  499 
0.  09  473 
0.  09  447 

9.  89  203 
9.  89  193 
9.  89  183 
9.89  173 
9.  89  162 

10 
10 
10 

11 

15 
14 
13 
12 
11 

25   0 

56 
52 
48 
44 

35  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  79  731 
9.  79  746 
9.79  762 
9.  79  778 
9.  79  793 

15 

16 
16 
15 

9.  90  578 
9.90  604 
9.  90  630 
9.90  656 
9.  90  682 

26 
26 
26 
26 

0.  09  422 
0.  09  396 
0.  09  370 
0.09  344 
0.  09  318 

9.89  152 
9.  89  142 
9.  89  132 
9.89  122 
9.89  112 

10 
10 
10 
10 

10 

9 

8 
7 
6 

24  40 
36 
32 
28 
24 

35  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  79  809 
9.  79  825 
9.  79  840 
9.  79  856 
9.  79  872 

16 
15 
16 
16 

9.90  708 
9.  90  734 
9,90  759 
9.90  785 
9.  90  811 

26 
25 
26 
26 

0.09  292 
0.  09  266 
0.  09  241 
0.  09  215 
0.09  189 

9.  89  101 
9.  89  091 
9.  89  081 
9.  89  071 
9.  89  060 

10 
10 
10 

11 

5 
4 
3 
2 

1 

24  20 
16 
12 
8 
4 

36   0 

60 

9.  79  887 

9.90  837 

0.09  163 

9.89  050 

0 

24   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

51° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  187 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  39° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

36   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  79  887 
9.79  903 
9.  79  918 
9.  79  934 
9.  79  950 

16 
15 
16 
16 
TS 

9.  90  837 
9.90  863 
9.  90  889 
9.90  914 
9.90  940 

26 
26 
25 
26 

0.09  163 
0.  09  137 
0.09  111 
0.  09  086 
0.  09  060 

9.  89  050 
9.  89  040 
9.  89  030 
9.  89  020 
9.  89  009 

10 
10 
10 
11 

60 

59 
58 
57 
56 

24   0 
56 
52 
48 
44 

36  20 
24 
28 
32 
36 

5 

6 
7 
8 
9 

9.79  965 
9.  79  981 
9.  79  996 
9.  80  012 
9.80  027 

16 
15 
16 
15 

9.  90  966 
9.90  992 
9.  91  018 
9.  91  043 
9.  91  069 

26 
26 
25 
26 

0.  09  034 
0.09  008 
0.  08  982 
0.  08  957 
0.  08  931 

9.88  999 
9.  88  989 
9.  88  978 
9.  88  968 
9.  88  958 

10 
11 
10 
10 

55 
54 

53 
52 
51 

23  40 
36 
32 
28 
24 

36  40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.80  043 
9.80  058 
9.  80  074 
9.  80  089 
9.80  105 

16 

16 
15 
16 

9.91  095 
9.91  121 
9.91  147 
9.91  172 
9.91  198 

26 
26 
25 
26 

0.08  905 
0.  08  879 
0.08853 
0.  08  828 
0.  08  802 

9.  88  948 
9.  88  937 
9.  88  927 
9.  88  917 
9.  83  906 

10 

11 

10 
10 

11 

50 

49 
48 
47 
46 

23  20 
16 
12 
8 
4 

37   0 
4 

8 
12 
16 

15 
16 
17 
18 
19 

9.80  120 
9.80  136 
9.80  151 
9.80  166 
9.80  182 

16 
15 
15 
16 

9.91  224 
9.  91  250 
9.91  276 
9.  91  301 
9.  91  327 

26 
26 
25 
26 

0.  08  776 
0.08  750 
0.  08  724 
0.  08  699 
0.  08  673 

9.88  896 
9.  88  886 
9.  88  875 
9.88  865 
9.88855 

10 
10 

11 

10 
10 

45 
44 
43 
42 
41 

23   0 
56 
52 
48 
44 

37  20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.80  197 
9.  80  213 
9.80  228 
9.80244 
9.80  259 

16 
15 
16 
15 

9.91  353 
9.91  379 
9.  91  404 
9.  91  430 
9,91  456 

26 
25 
26 
26 

0.08  647 
0.  08  621 
0.  08  596 
0.08  570 
0.08  644 

9.88  844 
9.  88  834 
9.  88  824 
9.88  813 
9.  88  803 

10 
10 

11 

10 

40 

39 
38 
37 
36 

22  40 
36 
32 

28 
24 

37  40 
44 
48 
52 
66 

25 
26 
27 
28 
29 

9.80  274 
9.80  290 
9.80  305 
9.80320 
9.80  336 

16 
15 
15 
16 

9.  91  482 
9.  91  507 
9.  91  533 
9.  91  559 
9.91  685 

25 
26 
23 
26 

0.  08  518 
0.  08  493 
0.  08  467 
0.08  441 
0.08  415 

9.88  793 
9.  88  782 
9.88  772 
9.88  761 
9.  88  751 

11 

10 

11 

10 

35 
34 
33 
32 
31 

22  20 
16 
12 
8 
4 

38   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.80  351 
9.80  366 
9.80  382 
9.  80  397 
9.80412 

15 
16 
15 
15 

9.91  610 
9.91  636 
9.91  662 
9.91  688 
9.91  713 

26 
26 
26 
25" 

0.08  390 
0.08  364 
0.  08  338 
0.08  312 
0.08287 

9.  88  741 
9.88  730 
9.  88  720 
9.  88  709 
9.  88  699 

11 

10 

11 

10 

30 

29 
28 
27 
26 

22   0 

56 
52 
48 
44 

38  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.80428 
9.  80  443 
9.80  458 
9.  80  473 
9.  80  489 

15 
15 
15 
16 

9.91  739 
9.91  765 
9.91  791 
9:91  816 
9.91  842 

26 
26 
25 
26 

0.  08  261 
0.  08  235 
0.  08  209 
0.  08  184 
0.08  158 

9.88  688 
9.  88  678 
9.  88  668 
9.88  657 
9.  88  647 

10 
10 

11 

10 

25 
24 
23 
22 
21 

21  40 
36 
32 

28 
24 

38  40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.80  504 
9.80519 
9.80  534 
9.80  550 
9.80  565 

15 
15 
16 
15 

1C 

9.91  868 
9.91  893 
9.91  919 
9.91  945 
9.  91  971 

25 
26 
26 
26 

0.  08  132 
0.08  107 
0.  08  081 
0.08  055 
0.  08  029 

9.  88  636 
9.  88  626 
9.88  615 
9.88  605 
9.88  594 

10 

11 

10 

11 

20 

19 
18 
17 
16 

21  20 
16 
12 
8 
4 

39   0 

4 
8 
12 
16 

45 

46 
47 

48 
49 

9.80  580 
9.80595 
9.80  610 
9.80  625 
9.80641 

15 
15 
15 
16 

9.91  996 
9.92  022 
9.  92  048 
9.  92  073 
9.92  099 

26 
26 
25 
26 

0.08  004 
0.07  978 
0.  07  952 
0.  07  927 
0.  07  901 

9.  88  684 
9.88  573 
9.  88  563 
9.  88  552 
9.  88  542 

11 

10" 
11 
10 

15 
14 
13 
12 
11 

21   0 

56 
58 
48 
44 

39  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.80656 
9.  80  671 
9.80  686 
9.  80  701 
9.80  716 

15 
15 
15 
15 

9.92  125 
9.92  150 
9.92  176 
9.92  202 
9.92227 

25 
26 
26 
25 

0.  07  875 
0.07  850 
0.07  824 
0.07  798 
0.07  773 

9.  88  531 
9.  88  521 
9.88  510 
9.88  499 
9.  88  489 

10 

11 
11 

10 

10 

9 

8 
7 
6 

20  40 
36 
32 
28 
24 

39  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.80  731 
9.  80  746 
9.  80  762 
9.  80  777 
9.80  792 

15 
16 
15 
16 

9.92  253 
9.  92  279 
9.92  304 
9.  92  330 
9.92  356 

26 
25 
26 
26 

0.07  747 
0.  07  721 
0.  07  696 
0.  07  670 
0.07  644 

9.  88  478 
9.88  468 
9.  88  457 
9.  88  447 
9.  88  436 

10 

11 

10 

u 

5 
4 
3 

1 

20  20 
16 
12 
8 
4 

40   0. 

60 

9.80  807 

9.92  381 

0.07  619 

9.  88  425 

0 

20   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  si 

50° 


188  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  40° 


m.  s. 

/ 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

40   0 
4 
S 
12 
16 

0 

1 
2 
3 
4 

9.  80  807 
9.  80  822 
9.  80  837 
9.80  852 
9.  80  867 

15 
15 
15 
15 
15 

15 
15 
15 
15 
15 

15 
15 
15 
15 
15 

15 
14 
15 
15 
15 

15 
15 
15 
15 
14 

15 
15 
15 
15 
14 

15 
15 
15 
15 
14 

15 
15 
14 
15 
15 

15 
14 
15 
15 
14 

15 
15 
14 
15 
15 

14 

15 
14 
15 
15 

14 
15 
14 
15 
14 

9.  92  381 
9.  92  407 
9.  92  433 
9.  92  458 
9.  92  484 

26 
26 
25 
26 
26 

25 
26 
26 
25 
26 

25 
26 
26 
25 
26 

26 
25 
26 
25 
26 

26 
25 
26 
25 
26 

26 
25 
26 
25 
26 

25 
26 
26 
25 
26 

25 
26 
25 
26 
26 

25 
26 
25 
26 
25 

26 
-25 
26 
26 
25 

26 
25 
26 
25 
26 

25 
26 
25 
26 
25 

0.07  619 
0.07  593 
0.07  567 
0.07  542 
0.07  516 

9.  88  425 
9.  88  415 
9.  88  404 
9.  88  394 
9.  88  383 

10 
11 
10 
11 
11 

10 
11 
11 
10 
11 

11 
10 
11 
11 
10 

11 
11 
10 
11 
11 

11 

10 

11 
11 

11 

10 

11 
11 
11 

10 

11 
11 
11 
11 

10 

11 
11 
11 
11 

11 

11 

10 

11 
11 
11 

11 
11 
11 
11 
11 

10 

11 
11 
11 
11 

11 
11 
11 
11 
11 

60 

59 

58 
57 
56 

20   0 
56 
52 

48 
44 

40  20 
24 
28 
32 
36 

5 
6 

8 
9 

9.80  882 
9.  80  897 
9.  80  912 
9.  80  927 
9.80  942 

9.  92  510 
9.  92  5a5 
9.  92  561 
9.  92  587 
9.  92  612 

0.  07  490 
0.07  465 
0.  07  439 
0.  07  413 

0.  07  388 

9.  88  372 
9.  88  362 
9.  88  351 
9.  88  340 
9.  88  330 

55 
54 
53 
52 
51 

19  40 
36 
32 
28 
24 

40  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  80  957 
9.  80  972 
9.  80  987 
9.  81  002 
9.  81  017 

9.  92  638 
9.  92  663 
9.  92  689 
9.92  715 
9.92  740 

0.  07  362 
0.07  337 
0.  07  311 
0.07  285 
0.  07  260 

9.  88  319 
9.88  308 
9.  88  298 
9.  88  287 
9.  88  276 

50 

49 
48 
47 
46 

19  20 
16 
12 
8 
4 

41   0 

8" 
12 
16 

15 
16 
17 
18 
19 

9.81  032 
9.  81  047 
9.  81  061 
9.81  076 
9.  81  091 

9.92  766 
9.  92  792 
9.  92  817 
9.  92  843 
9.  92  868 

0.07  234 
0.07  208 
0.07  183 
0.07  157 
0.07  132 

9.88  266 
9.  88  255 
9.  88  244 
9.  88  234 
9.88  223 

45 
44 
43 
42 
41 

19   0 
56 
52 
48 
44 

41  20 
24 

28 
32 
36 

20 

21 
22 
23 
24 

9.81  106 
9.81  121 
9.81  136 
9.81  151 
9.81  166 

9.  92  894 
9.  92  920 
9.  92  945 
9.92  971 
9.  92  996 

0.07  106 
0.07  080 
0.  07  055 
0.07  029 
0.  07  004 

9.  88  212 
9.  88  201 
9.  88  191 
9.88  180 
9.88  169 

40 

39 
38 
37 
36 

18  40 
36 
32 
28 
24 

41  40 

44 
48 
52 
56 

25 
26 
27 
28 
29 

9.81  180 
9.81  195 
9.  81  210 
9.81  225 
9.81  240 

9.93  022 
9.  93  048 
9.  93  073 
9.  93  099 
9.  93  124 

0.06  978 
0.06  952 
0.06  927 
0.  06  901 
0.  06  876 

9.  88  158 
9.  88  148 
9.  88  137 
9.88  126 
9.  88  115 

35 
34 
33 
32 
31 

18  20 
16 
12 
8 
4 

42   0 

4 
8 
12 
16 

30 

31 
32 
33 
34 

9.81  254 
9.  81  269 
9.  81  284 
9.81  299 
9.81  314 

9.  93  150 
9.93  175 
9.  93  201 
9.  93  227 
9.  93  252 

0.06  850 
0.  06  825 
0.  06  799 
0.  06  773 
0.06  748 

9.  88  105 
9.  88  094 
9.  88  083 
9.  88  072 
9.  88  061 

30 

29 
28 
27 
26 

18   0 
56 
52 
48 
44 

42  20 
24 

28 
32 
36 

35 
36 
37 
38 
39 

9.81  328 
9.  81  343 
9.81  358 
9.81  372 
9.81  387 

9.  93  278 
9.  93  303 
9.93  329 
9.  93  354 
9.  93  380 

0.06  722 
0.  06  697 
0.  06  671 
0.  06  646 
•0.06  620 

9.88  051 
9.88  040 
9.  88  029 
9.  88  018 
9.88  007 

25 
24 
23 
22 
21 

17  40 
36 
32 

28 
24 

42  40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.  81  402 
9.81  417 
9.  81  431 
9.81  446 
9.81  461 

9.93  406 
9.  93  431 
9.  93  457 
9.93  482 
9.  93  508 

0.06  594 
0.  06  569 
0.06  543 
0.  06  518 
0.06  492 

9.  87  996 
9.  87  m 
9.  87  975 
9.  87  964 
9.  87  953 

20 

19 
18 
17 
16 

17  20 
16 
12 
8  • 
4 

43   0 
4 
.  8 
12 
16 

45 
46 
47 
48 
49 

9.  81  475 
9.  81  490 
9.81  505 
9.81  519 
9.  81  534 

9.  93  533 
9.  93  559 
9.93  584 
9.93  610 
9.  93  636 

0.06  467 
0.06  441 
0.  06  416 
0.06  390 
0.06  364 

9.  87  942 
9-  87  931 
9.  87  920 
9.  87  909 
9.  87  898 

15 
14 
13 
12 
11 

17   0 
56 
52 
48 
44 

43  20 
24 

28 
32 
36 

50 

51 
52 
53 
54 

9.81  549 
9.  81  563 
9.  81  578 
9.81  592 
9.81  607 

9.  93  661 
9.  93  687 
9.  93  712 
9.  93  738 
9.  93  763 

0.06  339 
0.  06  313 
0.  06  288 
0.  06  262 
0.  06  237 

9.  87  887 
9.87  877 
9.87  866 
9.  87  855 
9.87  844 

10 

9 

8 
7 
6 

16  40 
36 
32 

28 
24 

43  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.81  622 
9.81  636 
9.81  651 
9.81  665 
9.  81  680 

9.  93  789 
9.93  814 
9.  93  840 
9.93  865 
9.  93  891 

0.  06  211 
0.06  186 
0.06  160 
0.06  IS) 
0.  06  109 

9.  87  833 
9.  87  822 
9.87  811 
9.87  800 
9.  87  789 

5 
4 
3 
2 

1 

16  20 
16 
12 
8 
4 

44   0 

60 

9.  81  694 

9.93  916 

C.06  084 

9.87  778 

0 

16   0 

L.COS. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin.. 

d. 

' 

m.  s 

49° 


GEOGRAPHIC    TABLES    AND    FORMULAS.  189 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  41o 


m.   s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.d. 

L.  Cotg. 

L.  Cos. 

d. 

44   0 
4 

8 
12 
16 

0 
1 

2 
3 
4 

9.  81  694 
9.  81  709 
9.81  723 
9.  81  738 
9.81  752 

15 
14 
15 
14 
15 

9.93  916 
9.93  942 
9.  93  967 
9.  93  993 
9.  94  018 

26 
25 
26 
25 
26 

0.06  084 
0.06  058 
0.  06  033 
0.06  007 
0.  05  982 

9.87  778 
9.  87  767 
9.  87  756 
9.  87  745 
9.87  734 

11 
11 
11 
11 
11 

60 

59 
58 
57 
56 

16   0 
56 
52 
48 
44 

44  20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  81  767 
9.81  781 
9.81  796 
9.81  810 
9.81  825 

14 

15 
14 
15 
14 

9.  94  044 
9.94069 
9.  94  095 
9.94  120 
9.  94  146 

25 
26 
25 
26 
25 

0.  05  956 
0.  05  931 
0.  05  905 
0.05  880 

I).  05  854 

9.  87  723 
9.  87  712 
9.  87  701 
9.87  690 
9.  87  679 

11 
11 
11 
11 
11 

55 
54 
53 
52 
51 

15  40 
36 
32 
28 
24 

44  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.81  839 
9.81  854 
9.  81  868 
9.  81  882 
9.81  897 

15 
14 
14 
15 
14 

9.  94  171 
9.94  197 
9.  94  222 
9.  94  248 
9.  94  273 

26 
25 
26 
25 
26 

0.  05  829 
0.05  803 
0.  05  778 
0.05  752 
0.  05  727 

9.  87  668 
9.  87  657 
9.  87  646 
9.87  635 
9.  87  624 

11 
11 
11 
11 
11 

50 

49 

48 
47 
46 

15  20 
16 
12 
8 
4 

45   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.81  911 
9.  81  926 
9.81  940 
9.81  955 
9.81  969 

15 
14 
15 
14 
14 

9.94  299 
9.  94  324 
9.  94  350 
9.  94  375 
9.  94  401 

25 
26 
25 
26 
25 

0.05  701 
0.  05  676 
0.  05  650 
0.  05  625 
0.  05  599 

9.  87  613 
9.  87  601 
9.  87  590 
9.87  579 
9.  87  568 

12 
11 
11 
11 
11 

45 
44 
43 
42 
41 

15   0 
56 
52 

48 
44 

45  20 

24 
1     28 
32 
36 

20 

21 
22 
23 
24 

9.81  983 
9.  81  998 
9.82  012 
9.  82  026 
9.  82  041 

15 
14 
14 
15 
14 

9.  94  426 
9.  94  462 
9.  94  477 
9.94  503 
9.94  528 

26 
25 
26 
25 
26 

0.05  574 
0.  05  548 
0.  05  523 
0.05497 
0.  05  472 

9.87  557 
9.  87  546 
9.87  535 
9.  87  524 
9.87  513 

11 
11 
11 
11 
\9. 

40 

39 
38 
37 
36 

14  40 
36 
32 
28 
24 

45  40 
44 
48 
52 
56 

25 
20 

27 
28 
29 

9.82  056 
9.  82  069 
9.82  084 
9.82  098 
9.  82  112 

14 
15 
14 
14 
14 

9.  94  554 
9.  94  579 
9.94  604 
9.94  630 
9.94  655 

25 
25 
26 
25 
26 

0.06  446 
0.  05  421 
0.06  396 
0.05  370 
0.  05  345 

9.  87  601 
9.  87  490 
9.  87  479 
9.87  468 
9.  87  457 

11 
11 
11 
11 
11 

35 
34 
33 
32 
31 

14  20 
16 
12 
8 
4 

46   0 

4 
8 
12 
16 

30 

31 
32 
33 
34 

9.82  126 
9.  82  141 
9.82  155 
9.82  169 
9.  82  184 

15 
14 
14 
15 
14 

9.94  681 
9.94  706 
9,94  732 
9.  94  757 
9.94  783 

25 
26 
25 
26 
25 

0.05  319 
0.  05  294 
0.  05  268 
0.  05  243 
0.  05  217 

9.  87  446 
9.  87  434 
9.  87  423 
9.87  412 
9.  87  401 

12 
11 
11 
11 
11 

30 

29 
28 
27 
26 

14   0 
56 
52 
48 
44 

46  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  82  198 
9.  82  212 
9.  82  226 
9.  82  240 
9.82  255 

14 
14 
14 
15 
14 

9.94  808 
9.  94  834 
9.  94  859 
9.  94  884 
9.94  910 

26 
25 
25 
26 
25 

0.05  192 
0.  05  166 
0.  05  141 
0.05  116 
0.05  090 

9.  87  390 
9.  87  378 
9.  87  367 
9.  87  356 
9.  87  345 

12 
11 
11 
11 
11 

25 
24 
23 
22 
21 

13  40 
36 

32 
28 
24 

46  40 
44 
48 
52 
56 

40 

41 
42 
43 

44 

9.82  269 
9.  82  283 
9.  82  297 
9.  82  311 
9.82326 

14 
14 
14 
15 
14 

9.94  935 
9.  94  961 
9.  94  986 
9.  95  012 
9.  95  037 

26 
25 
26 
25 
25 

0.05065 
0.  05  039 
0.05014 
0.04  988 
0.04963 

9.  87  334 
9.  87  322 
9.87  311 
9.87  300 
9.  87  288 

12 
11 
11 
12 
11 

20 

19 

18 
17 
16 

13  20 
16 
12 
8 
4 

47   0 

4 
8 
12 
16 

45 
46 
47 
48 
49 

9.82  340 
9.  82  354 
9.  82  368 
9.82  382 
9.  82  396 

14 
14 
14 
14 
14 

9.  95  062 
9.  95  088 
9.95  113 
9.95  139 
9.  95  164 

26 
25 
26 
25 
26 

0.  04  <«8 
0.  04  912 
0.04  887 
0.  04  861 
0.  04  836 

9.  87  277 
9.  87  266 
9.87  255 
9.87  243 
9.87  232 

11 
11 
12 
11 
11 

15 
14 
13 
12 
11 

13   0 

56 
52 
48 
44 

47  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  82  410 
9.  82  424 
9.  82  439 
9.  82  453 
9.  82  467 

14 
15 
14 
14 
14 

9.  95  190 
9.95  215 
9.  95  240 
9.  95  266 
9.  95  291 

25 
25 
26 
25 
°6 

0.04  810 
0.04  785 
0.04  760 
0.  04  734 
0.04  709 

9.  87  221 
9.  87  209 
9.87  198 
9.87  187 
9.87  175 

12 
11 
11 
12 
11 

10 

9 

8 
7 
6 

12  40 
36 
32 
28 
24 

47  40 
44 
48 
52 
56 

55 

56 
57 
58 
59 

9.  82  481 
9.  82  495 
9.82  509 
9.  82  523 
9.82  537 

14 
14 
14 
14 
14 

9.  95  317 
9.95  342 
9.  95  368 
9.  95  393 
9.95418 

25 
26 
25 
25 
26 

0.04683 
0.  04  658 
0.  04  632 
0.  04  607 
0.  04  582 

9.87  164 
9.87  153 
9.87  141 
9.87  130 
9.87  119 

11 
12 
11 
11 
12 

5 
4 
3 
2 
1 

12  20 
16 
12 
8 
4 

48   0 

60 

9.82  551 

9.  95  444 

0.  04  556 

9.  87  107 

0 

12   0 

L.  Cos. 

d. 

L.  Cotg. 

c.d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

48° 


190  GEOGEAPHIC    TABLES    AND    FORMULAS. 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 
2h  42° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

48   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  82  551 
9.  82  565 
9.  82  579 
9.  82  593 
9.  82  607 

14 
14 
14 
14 
14 

9.95  444 
9.  95  469 
9.  95  495 
9.  95  520 
9.  95  545 

25 
26 
25 
25 
26 

0.  04  556 
0.04  531 
0.  04  505 
0.  04  480 
0.  04  455 

9.87  107 
9.  87  096 
9.  87  085 
9.  87  073 
9.  87  062 

11 
11 
12 
11 
T> 

60 

59 

58 
57 
56 

12   0 
56 
52 

48 
44 

48   20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  82  621 
9.  82  635 
9.  82  649 
9.  82  663 
9.  82  677 

14 
14 
14 
14 
14 

9.  95  571 
9.  95  596 
9.  95  622 
9.  95  647 
9.  95  672 

25 
26 
25 
25 
26 

0.  04  429 
0.  04  404 
0.  04  378 
0.  04  353 
0.  04  328 

9.87  050 
9.  87  039 
9.  87  028 
9.87  016 
9.  87  005 

11 
11 
12 
11 
12 

55 
54 
53 
52 
51 

11   40 
36 
32 
28 
24 

48   40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.  82  691 
9.  82  705 
9.82  719 
9.  82  733 

9.  82  747 

14 
14 
14 
14 
14 

9.  95  698 
9.  95  723 
9.  95  748 
9.  95  774 
9.  95  799 

25 
25 
26 
25 
26 

0.  04  302 
0.  04  277 
0.  04  252 
0.  04  226 
0.  04  201 

9.  86  993 
9.  86  982 
9.  86  970 
9.  86  959 
9.  86  947 

11 
12 
11 
12 
11 

50 

49 
48 
47 
46 

11   20 
16 
12 
8 
4 

49   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.  82  761 
9.82  775 
9.  82  788 
9.  82  802 
9.  82  816 

14 
13 
14 
14 
14 

9.  95  825 
9.  95  .850 
9.  95  875 
9.  95  901 
9.  95  926 

25 
25 
26 
25 
26 

0.04  175 
0.  04  150 
0.04  125 
0.  04  099 
0.  04  074 

9.  86  936 
9.  86  924 
9.  86  913 
9.  86  902 
9.  86  890 

12 
11 
11 
12 
11 

45 
44 
43 
42 
41 

11   0 
56 
52 

48 
44 

49   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.  82  830. 
9.  82  844 
9.  82  858 
9.82  872 
8.82.885 

14 
14 
14 
13 
14 

9.  95  952 
9.  95  977 
9.  96  002 
9.  96  028 
9.  96  053 

25 

25 
26 
25 
25 

0.04  048 
0.  04  023 
0.03  998 
0.  03  672 
0.  03  947 

9.  86  879 
9.  86  867 
9.  86  855 
9.  86  844 
9.  86  832 

12 
12 
11 
12 
11 

40 

39 
38 
37 
36 

10   40 
36 
32 

28 
24 

49   40 
44 

48 
52 
56 

25 
26 
27 
28 
29 

9.  82  899 
9.  82  913 
9.  82  927 
9.  82  941 
9.  82  955 

14 
14 
14 
14 
13 

9.  96  078 
9.  96  104 
9.96  129 
9.96  155 
9.  96  180 

26 
25 
26 
25 
25 

0.  03  922 
0.  03  896 
0.  03  871 
0.  03  845 
0.  03  820 

9.  86  821 
9.  86  809 
9.  86  798 
9.  86  786 
9.86  775 

12 
11 
12 
11 
12 

35 
34 
33 
32 
31 

10   20 
16 
12 

8 

4 

50   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.  82  968 
9.  82  982 
9.  82  996 
9.  83  010 
9.  83  023 

14 
14 
14 
13 
14 

9.  96  205 
9.  96  231 
9.96  256 
9.  96  281 
9.  96  307 

26 
25 
25 
26 

25 

0.  03  795 
0.03  769 
0.  03  744 
0.  03  719 
0.  03  693 

9.  86  763 
9.  86  752 
9.86  740 
9.  86  728 
9.86  717 

11 
12 
12 
11 
V? 

30 

29 

28 
27 
26 

10   0 
56 
52 
48 
44 

50   20 
24 

28 
32 
36 

35 
36 
37 
38 
39 

9.  83  037 
9.63  051 
9.83  065 
9.  83  078 
9.  83  092 

14 
14 
13 
14 
14 

9.  96  332 
9.96  357 
9.  96  383 
9.  96  408 
9.  96  433 

25 
26 
25 
25 
26 

0.  03  668 
0.  03  643 
0.  03  617 
0.  03  592 
0.03  567 

9.  86  705 
9.86  694 
9.  86  682 
9.  86  670 
9.  86  659 

11 
12 
12 
11 

25 
24 
23 
22 
21 

9   40 
36 
32 
28 
24 

50   40 
44 

48 
52 
56 

40 

41 
42 
43 
44 

9.83  106 
9.  83  120 
9.83  133 
9.  83  147 
9.83  161 

14 
13 
14 
14 
13 

9.  96  459 
9.  96  484 
9.96  510 
9.  96  535 
9.96  560 

25 
26 
25 
25 
26 

0.  03  541 
0.03  516 
0.  03  490 
0.  03  465 
0.  03  440 

9.  86  647 
9.  86  635 
9.  86  624 
9.  86  612 
9.  86  600 

12 
11 
12 
12 
11 

20 

19 
18 
17 
16 

9   20 
16 
12 
8 
4 

51   0 
4 
8 
12 
16 

45 
46 
47 

48 
49 

9.83  174 
9.83  188 
9.83  202 
9.  83  215 
9.  83  229 

14 
14 
13 
14 
13 

9.  96  586 
9.96  611 
9  96  636 
9.  96  662 
9.  96  687 

25 
25 
26 
25 
25 

0.  03  414 
0.03  389 
0.  03  3(54 
0.03  338 
0.  03  313 

9.  86  589 
9.  86  577 
9.  86  565 
9.  86  554 
9.  86  542 

12 
12 
11 
12 
12 

15 
14 
13 
12 
11 

9   0 
56 
52 
48 
44 

51   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  83  242 
9.  83  256 
9.  83  270 
9.  83  283 
9.  83  297 

14 
14 
13 
14 
13 

9.  96  712 
9.  96  738 
9.  96  763 
9.  96  788 
9.  96  814 

26 
25 
25 
26 
25 

0.  03  288 
0.  03  262 
0.  03  237 
0.  03  212 
0.03  186 

9.  86  530 
9.  86  518 
9.  86  507 
9.  86  495 
9.  86  483 

12 
11 
12 
12 
11 

10 

9 

8 
7 
6 

8   40 
36 
32 
28 
2* 

51   40 

44 
48 
52 
56 

55 
56 
57 

58 
59 

9.83  310 
9.  83  324 
9  83  338 
9.  83  351 
9,  83  365 

14 
14 
13 
14 
13 

9.  96  839 
9.  96  864 
9.  96  890 
9.96  915 
9.  96  940 

25 
26 
25 
25 
26 

0  03  161 
0  03  136 
0.03  110 
0.  03  085 
0.  03  060 

9.  86  472 
9.86  460 
9.86  448 
9.  86  436 
9.  86  425 

12 
12 
12 
11 
12 

5 
4 
3 
2 
1 

8   20 
16 
12 
8 
4 

52   0 

60 

9.  83  378 

9.96  966 

0.  03  034 

9.86  413 

0 

8   0 

L.  Cos. 

d. 

L.Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

47' 


GEOGRAPHIC    TABLES    AND    FORMULAS.  191 

TABLE  22. — Five-place  logarithms  of  circular  functions,  etc. — Continued. 

2h  43° 


m.  8. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

52   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.83  378 
9.83  392 
9.83  405 
9.  83  419 
9.  83  432 

14 
13 
14 
13 
14 

9.96  966 
9.96  991 
9.  97  016 
9.  97  042 
9.97  067. 

25 
25 
26 
25 
25 

0.  03  034 
0.  03  009 
0.  02  984 
0.  02  958 
0.02  933 

9.  86  413 
9.86401 
9.  86  389 
9.  86  377 
9.  86  366 

12 
12 
12 
11 
T> 

GO 

59 
58 
57 
56 

8    0 
56 
52 
48 
44 

52   20 
24 
28 
32 
36 

5 

6 
7 
8 
9 

9.83  446 
9.  83  459 
9.  83  473 
9.83  486 
9.83  500 

13 
14 
13 
14 
13 

9.  97  092 
9.  97  118 
9.  97  143 
9.97  168 
9.97  193 

26 
25 
25 
25 
26 

0.  02  908 
0.  02  882 
0.  02  857 
0.  02  832 
0.  02  807 

9.  86  354 
9.  86  342 
9.  86  330 
9.  86  318 
9.  86  306 

12 
12 
12 
12 
11 

55 
54 
53 
52 
51 

7   40 
36 
32 
28 
24 

52   40 
44 
48 
52 
56 

10 

11 
12 
13 
14 

9.83  513 
9.83  527 
9.  83  540 
9.83  554 
9.83  567 

14 
13 
14 
13 
14 

9.  97  219 
9.  97  244 
9.97  269 
9.  97  295 
9.  97  320 

25 
25 
26 
25 
25 

0.02  781 
0.02  756 
0.02  731 
0.02  705 
0.  02  680 

9.  86  295 
9.  86  283 
9.  86  271 
9.  86  259 
9.  86  247 

12 
12 
12 
12 
1? 

50 

49 
48 
47 
46 

7   20 
16 
12 

8 
4 

53   0 
4 
8 
12 
16 

15 
16 
17 
18 
19 

9.83  581 
9.83  594 
9.  83  608 
9.  83  621 
9.  83  634 

13 
14 
13 
13 
14 

9.  97  345 
9.  97  371 
9.97  396 
9.97  421 
9.  97  447 

26 
25 
25 
26 
25 

0.02  655 
0.  02  629 
0.  02  604 
0.02  579 
0.  02  553 

9.86  235 
9.  86  223 
9.86  211 
9.86  200 
9.86  188 

12 
12 
11 
12 
12 

45 
44 
43 
42 
41 

7    0 
56 
52 
48 
44 

53   20 
24 
28 
32 
36 

20 

21 
22 
23 
24 

9.83  648 
9.  83  661 
9.  83  674 
9.83  688 
9.  83  701 

13 
13 
14 
13 
14 

9.97  472 
9.  97  497 
9.97  523 
'.).  97  5  18 
9.97  573 

25 
26 
25 

25' 
25 

0.  02  528 
0.02  503 
0.02  477 
0.  02  452 

0.02  427 

9.86  176 
9.  86  164 
9.86  152 
9.  86  140 
9.  86  128 

12 
12 
12 
12 
V? 

40 

39 
38 
37 
36 

6   40 
36 
•   32 

28 
24 

53   40 
44 

48 
52 
56 

25 
26 
27 

28 
29 

9.83  715 
9.  83  728 
9.83  741 
9.83  755 
9.  83  768 

13 
13 
14 
13 
13 

9.  97  598 
9.97  624 
9.  97  649 
9.97  674 
9.97  700 

26 
25 
25 
26 
25 

0.  02  402 
0.02  376 
0.  02  351 
0.  02  326 
0.02  300 

9.  86  116 
9.  86  104 
9.  86  092 
9.86  080 
9.  86  068 

12 
12 
12 
12 
12 

35 
34 
33 
32 
31 

6   20 
16 
12 

8 
4 

54   0 
4 
8 
12 

16 

30 

31 
32 
33 
34 

9.83  781 
9.83  795 
9.83  808 
9.83  821 
9.83  834 

14 
13 
13 
13 
14 

9.  97  725 
9.97  750 
9.97  776 
9.97  801 
9.  97  826 

25 
26 
25 
25 
25 

0.  02  275 
0.02  250 
0.02  224 
0.02  199 
0.02  174 

9.  86  056 
9.86  044 
9.  86  032 
9.  86  020 
9.86  008 

12 
12 
12 
12 
12 

30 

29 
28 
27 
26 

6    0 
56 

52 
48 
44 

54   20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  83  848 
9.83  861 
9.83  874' 
9.  83  887 
9.83901 

13 
13 
13 

14 
13 

9.  97  851 
9.  97  877 
9.  97  902 
9.  97  927 
9.97  953 

26 
25 
25 
26 
25 

0.02  149 
0.02  123 
0.02  098 
0.  02  073 
0.  02  047 

9.  86  996 
9.  85  984 
9.85  972 
9.  85  960 
9.  85  948 

12 
12 
12 
12 
19, 

25 
24 
23 
22 
21 

5   40 
36 
32 

28 
24 

54   40 
44 
48 
52 
56 

40 

41 
42 
43 
44 

9.83  914 
9.  83  927 
9.  83  940 
9.  83  954 
9.  83  967 

13 
13 
14 
13 
13 

9.97  978 
9.98  003 
9.98  029 
9.  98  054 
9.  98  079 

25 
26 
25 
25 
25 

0.  02  022 
0.01  997 
0.01  971 
0.01  946 
0.01  921 

9.  85  936 
9.  85  924 
9.  85  912 
9.  85  900 
9.  85  888 

12 
12 
12 
12 
12 

20 

19 

18 
17 
16 

5   20 
16 
12 

8 
4 

55   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.83  980 
9.83  993 
9.84  006 
9.  84  020 
9.  84  033 

13 
13 
14 
13 
13 

9.98  104 
9.  98  130 
9.  98  155 
9.  98  180 
9.  98  206 

26 
25 
25 
26 
25 

0.  01  896 
0.01  870 
0.01  845 
0.  01  820 
0.01  794 

9.  85  876 
9.  85  864 
9.  85  851 
9.  85  839 
9.85827 

12 
13 
12 
12 
12 

15 
14 
13 
12 
11 

5    0 
56 
52 

48 
44 

55   20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  84  046 
9.  84  059 
9.  84  072 
9.84  085 
9.84  098 

13 
13 
13 
13 
14 

9.  98  231 
9.  98  256 
9.  98  281 
9.  98  307 
9.  98  332 

25 
25 
26 
25 
25 

0.  01  769 
0.01  744 
0.01  719 
0.01  693 
0.01  668 

9.85815 
9.  85  803 
9.  85  791 
9.  85  779 
9.  85  766 

12 
12 
12 
13 
12 

10 

9 

8 
7 
6 

4   40 

36 
32 
28 
24 

55   40 
44 
48 
52 
56 

55 
56 
57 

58 
59 

9.84  112 
9.84  125 
9.84  138 
9.  84  151 
9.  84  164 

13 
13 
13 
13 
13 

9.  98  357 
9.  98  383 
9.  98  408 
9.  98  433 
9.  98  458 

26 
25 
25 
25 
26 

0.  01  643 
0.01  617 
0.  01  592 
0.  01  567 
0.01  542 

9.  85  754 

9.  85  742 
9.  85  730 
9.85  718 
9.  85  706 

12 
12 
12 
12 
13 

5 
4 

3 
2 
1 

4   20 
16 
12 

8 
4 

56   0 

00 

.9.84  177 

9.  98  484 

0.  01  516 

9.  85  693 

0 

4    0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/ 

m.  s. 

192  GEOGKAPHIC  TABLES  AND  FORMULAS. 

TABLE  22. — Five-pl&ce  logarithms  of  circular  functions,  etc. — Continued. 
2h  44° 


m.  s. 

' 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

56   0 
4 
8 
12 
16 

0 

1 
2 
3 
4 

9.  84  177 
9.  84  190 
9.  84  203 
9.  84  216 
9.  84  229 

13 
13 
13 
13 
13 

9.  98  484 
9.  98  509 
9.  98  534 
9.  98  560 
9.98  585 

25 
25 
26 
25 
25 

0.01  516 
0.01  491 
0.01  466 
0.01  440 
0.01  415 

9.  85  693 
9.  85  681 
9.  85  669 
9.  85  657 
9.  85  645 

12 
12 
12 
12 
13 

60 

59 

58 
57 
56 

4   0 

"56 
52 
48 
44 

56  20 
24 
28 
32 
36 

5 
6 
7 
8 
9 

9.  84  242 

9.  84  255 
9.  84  269 
9.  84  282 
9.  84  295 

13 
14 
13 
13 
13 

9.98  610 
9.  98  635 
9.  98  661 
9.  98  686 
9.  98  711 

25 
26 
25 
25 
26 

0.01  390 
0.01  365 
0.01  339 
0.01  314 
0.01  289 

9.  85  632 
9.  85  620 
9.  85  608 
9.  85  596 
9.  85  583 

12 
12 
12 
13 
12 

55 
54 
53 
52 
51 

3  40 
36 
32 

28 
24 

56  40 
44 

48 
52 
56 

10 

11 
12 
13 
14 

9.  84  308 
9.  84  321 
9.84  334 
9.  84  347 
9.84360 

13 
13 
13 
13 
13 

9.  98  737 
9.  98  762 
9.98  787 
9.  98  812 
9.98  838 

25 
25 
25 
26 
25 

0.  01  263 
0.  01  238 
0.  01  213 
0.01  188 
0.01  162 

9.  85  571 
9.  85  559 
9.  85  547 
9.  85  534 
9.  85  522 

12 
12 
13 
12 
12 

50 

49 
48 
47 
46 

3  20 
16 
12 
8 
4 

57   0 
4 
8 
12 
16 

15 
J6 
17 
18 
19 

9.  84  373 
9.84  385 
9.  84  398 
9.  84  411 
9.  84  424 

12 
13 
13 
13 
13 

9.  98  863 
9.  98  888 
9.98  913 
9.  98  939 
9.  98  964 

25 
25 
26 
25 
25 

0.01  137 
0.01  112 
0.  01  087 
0.01  061 
0.  01  036 

9.  85  510 
9.  85  497 
9.85  485 
9.  85  473 
9.85460 

13 
12 
12 
13 
12 

45 
44 
43 
42 
41 

3   0 

56 
52 
48 
44 

57  20 
24 
•28 
32 
36 

20 

21 
22 
23 
24 

9.  84  437 
9.  84  450 
9.  84  463 
9.  84  476 
9.  84  499 

13 
13 
13 
13 
13 

9.  98  989 
9.  99  015 
9.  99  040 
9.99  065 
9.  99  090 

26 
25 
25 
25 
26 

0.01  Oil 
0.00  985 
0.  00  960 
0.00  935 
0.00  910 

9.  85  448 
9.  85  436 
9.  85  423 
9.  85  411 
9.  85  399 

12 
13 
12 
12 
13 

40 

39 
38 
37 
36 

2  40 
36 
32 

28 
24 

57  40 
44 
48 
52 
56 

25 
26 

27 
28 
29 

9.  84  502 
9.  84  515 
9.  84  528 
9.  84  540 
9.  84  553 

13 
13 
12 
13 
13 

9.99  116 
9.  99  141 
9.  99  166 
9.99  191 
9.  99  217 

25 
25 
25 
26 
25 

0.  00  884 
0.00859 
0.  00  834 
0.  00  809 
0.  00  783 

9.  85  386 
9.  85  374 
9.  85  361 
9.  85  349 
9.  85  337 

12 
13 
12 
12 
13 

35 
34 
33 
32 
31 

2  20 
16 
12 
8 
4 

58   0 
4 
8 
12 
16 

30 

31 
32 
33 
34 

9.84  566 
9.  84  579 
9.  84  592 
9.  84  605 
9.84  618 

13 
13 
13 
13 
12 

9.  99  242 
9.  99  267 
9.  99  293 
9.  99  318 
9.  99  343 

25 
26 
25 
25 
25 

0.00  758 
0.00  733 
0.  00  707 
0.00  682 
0.  00  657 

9.  85  324 
9.  85  312 
9.85  299 
9.  85  287 
9.  85  274 

12 
13 
12 
13 

12 

30 

29 
28 
27 
26 

2   0 

56 
52 
48 
44 

58  20 
24 
28 
32 
36 

35 
36 
37 
38 
39 

9.  84  630 
9.  84  643 
9.84  656 
9.  84  669 
9.  84  682 

13 
13 
13 
13 
12 

9.  99  368 
9.  99  394 
9.  99  419 
9.  99  444 
9.  99  469 

26 
25 
25 
25 
26 

0.  00  632 
0.  00  606 
0.  00  581 
0.  00  556 
0.  00  531 

9.  85  262 
9.85  250 
9.  85  237 
9.  85  225 
9.  85  212 

12 
13 
12 
13 
12 

25 
24 
23 
22 
21 

1  40 
36 
32 

28 
24 

58  40 
44 
48 
52 
56 

40 

41 
42 
43 

44 

9.  84  694 
9.  84  707 
9.84  720 
9.84  733 
9.84  745 

13 
13 
13 
12 
13 

9.99  495 
9.  99  520 
9.  99  545 
9.  99  570 
9.  99  596 

25 
25 
25 
26 
25 

0.  00  505 
0.00  480 
0.  00  455 
0.  00  430 
0.00  404 

9.  85  200 
9.  85  187 
9.85  175 
9.  85  162 
9.  85  150 

13 
12 
13 
12 
13 

20 

19 
18 
17 
16 

1  20 
16 
12 

8 
4 

59   0 
4 
8 
12 
16 

45 
46 
47 
48 
49 

9.84  758 
9.  84  771 
9.84  784 
9.  84  796 
9.  84  809 

13 
13 
12 
13 
13 

9.  99  621 
9.  99  646 
9.  99  672 
9.  99  697 
9.  99  722 

25 
26 
25 
25 
25 

0.00  379 
0.00  354 
0.  00  328 
0.  00  303 
0.  00  278 

9.  85  137 
9.85  125 
9.85  112 
9.  85  100 
9.85  087 

12 
13 
12 
13 
13 

15 
14 
13 
12 
11 

1   0 

56 
52 
48 
44 

59  20 
24 
28 
32 
36 

50 

51 
52 
53 
54 

9.  84  822 
9.  84  835 
9.  84  847 
9.84  860 
9.  84  873 

13 
12 
13 
13 

12 

9.99  747 
9.  99  773 
9.  99  798 
9.99  823 
9.  99  848 

26 
.25 
25 
25 
26 

0.  00  253 
0.  00  227 
0.00202 
0.00  177 
0.00  152 

9.  85  074 
9.  85  062 
9.  85  049 
9.  85  037 
9.  85  024 

12 

13 
12 
13 
12 

10 

9 

8 

6 

0  40 
36 
32 
28 
24 

59  40 
44 
48 
52 
56 

55 
56 
57 
58 
59 

9.  84  885 
9.  84  898 
9.  84  911 
9.  84  923 
9.  84  936 

13 
13 
12 
13 
13 

9.  99  874 
9.  99  899 
9.99  924 
9.  99  949 
9.  99  975 

25 
25 
25 
26 
25 

0.  00  126 
0.  00  101 
0.  00  076 
0.  00  051 
0.00  025 

9.  85  012 
9.  84  999 
9.  84  986 
9.  84  974 
9.  84  961 

13 
13 
12 
13 
12 

5 
4 
3 
2 
1 

0  20 
16 
12 
8 
4 

60   0 

60 

9.  84  949 

0.00  000 

0.00  000 

9.  84  949 

0 

0   0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

' 

m.  s. 

45C 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


193 


TABLE  23. — GEODETIC  POSITION  COMPUTATIONS. 

TABLE  OF  LOGARITHMS  OF  FACTORS  A,  B,  C,  D,  E,  F^  BASED  UPON  THE  CLARKE  SPHE- 
ROID OF  1866  AND  THE  METRIC  SYSTEM,  BETWEEN  LATITUDES  0°  AND  72°. 

[Extracted  from  reports  of  the  U.  S.  Coast  and  Geodetic  Survey.] 
CONSTANTS. 


A  = 


~ 


(1  — g2sin2  <?)* 
a  arc  l// 


a  (1  —  e2)  arc  1" 


(1  —  (?  sin2  cp)2  tan  cp 
~~    2a2  (I  —  /)  arcl" 
_  f  &  sin  cp  cos  cp  arc  \" 

1  —  e2  sin2  cp 
(1  +  3  tan2  cp)  (I  —  e2  sin2  cp) 

F  =  y^-  sin  cp  cos2  cp  arc2  1" 


log 


log  a  =  6.804  698  57 

log  b  =  6.803  223  78 

log  e*  =  7.830  502  57 

77=8X509  726  56 


a  arc  1 


lQga(l-^)ar^  =  5-51267615 
1 


log; 


=  1.406  947  6 


2a2  (1  —  e2)  arcl/x 
log  (f  e2  arc  lx/)  =2.692  168  7 

log  ^  =  5.612  45 
log  (TVarc2  1")  =  8.291  96 


Ratio  adopted  in  this  table  is  the  Clarke  value  of  the  meter,  namely,  1  meter  = 
39.370432  inches. 

The  formulas  for  the  computation  of  the  geodetic  differences  in  latitude  Acp,  in 
longitude  AX,  and  in  azimuth  Aa  are  as  follows: 

{—Acp=s  cos  a  .  B+s2  sin2  a  .  C+(6<p)2  D—  h  .  s2  sin2  a  .  E 
AX=s  sin  a  sec  <?/  .  A 
-Aa=AX  sin  $  (<p+g/)  sec  £  (^/<p)+(  ^A)3  F 
where 


g/--= 
A/= 
a'= 


A  and  f  —  <5<p=s  cos  a  .  ^+s2  sin2  a  .  C—  h  .  S*  sin2  a  .  E 

a=a        a+180  t         also  A=«  cos  a  .  J? 

For  subordinate  triangulation  when  the  sides  do  not  exceed  say  25  kilometers,  or 
about  15  statute  miles,  the  term  involving  E  in  Acp  and  the  factor  sec  \  (Acp},  as 
well  as  the  term  involving  j^in  A  a,  may  be  omitted. 

46061—08  -  13 


194 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


EXAMPLES    OF    COMPUTATION    OF    GEODETIC    COORDINATES. 


Azimuth  a:               Nell  —  ( 
Spherical  angle: 

Azimuth  a7:             Nell  —  5 
d  a+180° 

Azimuth  (a):            Zuni  — 
Latitude. 

0                /                  // 

0:       35     25     13.473                         Nell. 
d  (p         -17    47.546               Geo.  Pos.  No 

0                  /                     // 

^husca.        159     29     08.728 
120     54     13.980                  » 

5uni.              38     34     54.748 
179     50    02.  124 

Nell.            218     24     56.872 
Longitude. 

o             /        // 

A:                          108     37     24.925 
.5.               d  A                       +17     15.  360 

07      35    07     25.927                         Zuni. 
Geo.  Pos.  No 
Computation  for 
latitude: 

log  s             4.  6236305 
"    B           8.5111933 
"    cos  a7     9.8930500 

log  (I)          3.  0278738 

log  s2               9.  24726 
"   C               1.25696 
"    sinV        9.58986 

log  (II)           0.  09408 

A7                      108     54    40.285 
.  6. 
Computation  for  longitude: 

log  s                                 4.  6236305 
"    sin  a7                         9.7949286 
"A7                               8.5092394 
"    sec  0                        0.0872944 
Corr.  for  diff.  arc  &  sine=  —  15 

log  (V)                             3.  0150914 
d  A                                   103577.360 

Computation  of  azimuth: 
log  (V)                              3.  015091 

"   sin             \^~2j  9.761522 
f  dd>   \ 

"    df>n                 (                    10   000001 

log  D                 2.  3674 
"    [I+II]2       6.0568 

log  (III)           8.4242 

log  E                 6.  0124 
14   s2sinV       8.8371 
"    (I)               3.0279 

log  (VI)                             2.  776614 
da                              -     59777.876 
-97    5777.876 

Azimuth  check. 

log  (IV)            7.  8774 

(I)            1066.286+  \ 
(II)                 1.242+  i 

(III)                .026+           [I+H]  1067.528 
(IV)                 .008-     log       "            3.028 
f  m-TTl2        6.056 

3792  Check: 
7584  Snher.  anffle 

GEOGRAPHIC  TABLES  AND  FORMULAS. 


195 


Azimuth  a:               Chusca 
Spherical  angle: 

Azimuth  ax:              Chusca 
da  +180° 

Azimuth  (a)  :            Zuni— 
Latitude. 

o         /             // 

0:       35     53    06.746                      Chusca. 
d(p    —    45    40.818             Geo.  Pos.  No 

0               /                   // 

—Nell.         339    21    40.150 
25     11    38.  601 

—Zuni.            4    33     18.751 
179     57     25.  650 

Chusca.        184     30    44.401 
Longitude. 

0                /                     // 

A:                          108     50     14.518 
.4.              dh                             +4     25.768 

(f>/      35    07     25.928                        Zuni. 
Geo.  Pos.  No 
Computation  for 
latitude: 

log  s            4.  9280539 
"  B             8.5111594 
"    cosax    9.9986260 

A/                         108     54    40.286 
.  6. 
Computation  for  longitude: 

log  s                                4.  9280539 
"   sina'                         8.8999280 
"    A'                              8.5092394 
"   sec  <£x                       0.0872944 

log  (I)         3.4378393 

log  (V)                            2.  4245028 
dl                                +265/x.768 

Computation  of  azimuth: 

log  (V)                              2.  424503 
"   Bin(£±^)            9.764002 

"  <?pp  (  ^  ^  ~\         o  oooooq  . 

log  s2               9.  85610 
"   C                1.26435 
"   sin2ax       7.79982 

log  (II)           8.  92027 

log  D                 2.  3698 

"    [L+II]2       6.8757 

log  (III)           9.  2460 

log  E                 6.  0214 
"   s2sin2ax       7.6559 
"    (I)               3.4378 

log  (VI)                            2.  188514 
da                           -      154/x.  350 
-2X    34X/.350 

Azimuth  check: 

O               /                   ff 

218     24     56.  872 
184     30     44  401 

log  (IV)            7.  1151 
// 

(I)           2740.560+  j 
(II)                 .083+4 

(III)               .176+   i         [I+H]   2740.64 
(IV)                .001-     log       "              3.43 
•'    TT  1  TTT-         (\  <37 

0 

78525     Check:                         33     54     12.471 
5705      Spher.  angle 
at  Zuni                     33     54     12.469 

—dL  +2740.818 

196 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  0°. 


Lat. 

log  A 

logB 

logC 

logJD 

logE 

logF 

o   / 

00  00 

8.  509  7266 

8.512  6761 

_-oo 

_-00 

5.  6125 

-00 

1 

66 

61 

2-  8707 

9.156 

5 

2 

66 

61 

8.  1717 

457 

5 

3 

66 

61 

3477 

633 

5 

4 

66 

61 

4727 

758 

5 

05 

66 

61 

5696 

_  855 

5 

6 

66 

61 

6488 

9.934 

5 

7 

66 

61 

7158 

0.001 

5 

8 

66 

61 

7740 

059 

5 

9 

66 

61 

8249 

110 

5 

10 

8.509  7266 

8.512  6761 

8.  8707 

0.156 

5.6125 

11 

65 

61 

9121 

197 

5 

12 

65 

61 

9499 

235 

5 

13 

65 

61 

8.  9846 

270 

5 

14 

65 

61 

9.0168 

302 

5 

15 

65 

61 

0468 

332 

5 

16 

65 

61 

0748 

360 

5 

17 

65 

60 

1011 

386 

5 

18 

65 

60 

1259 

411 

5 

19 

65 

60 

1494 

435 

5 

20 

8.509  7265 

8.  512  6760 

9.  1717 

0.457 

5.  6125 

6.057 

21 

65 

60 

1929 

478 

5 

22 

65 

60 

2131 

498 

5 

23 

65 

60 

2324 

518 

5 

24 

65 

59 

2509 

536 

5 

25 

65 

59 

2686 

554 

5 

26 

65 

59 

2S57 

571 

5 

27 

65 

59 

3020 

587 

5 

28 

55 

59 

3178 

603 

5 

29 

65 

58 

3331 

618 

5 

30 

8.  509  7265 

8.  512  6758 

9.  3478 

0.633 

5.6126 

31 

64 

58 

3620 

647 

6 

32 

64 

58 

3758 

661 

6 

33 

64 

57 

9.  3892 

674 

6 

34 

64 

57 

9.4022* 

687 

6 

35 

64 

57 

4148 

700 

6 

36 

64 

57 

4270 

712 

6 

37 

64 

56 

4389 

724 

6 

38 

64 

56 

4505 

736 

6 

39 

64 

56 

4618 

747 

6 

40 

8.  509  7264 

8.  512  6756 

9.  4728 

0.758 

5.  6126 

6.358 

41 

64 

55 

4835 

769 

6 

42 

64 

55 

9.  4939 

779 

6 

43 

64 

55 

9.  5042 

789 

6 

44 

63 

54 

5141 

799 

7 

45 

63 

54 

5239 

809 

7 

46 

63 

54 

5335 

819 

7 

47 

63 

53 

5428 

828 

7 

48 

63 

53 

5519 

837 

7 

49 

63 

53 

5609 

846 

7 

50 

8.  509  7263 

8.  512  6752 

9.  5697 

0.855 

5.  6127 

51 

63 

52 

5783 

863 

7 

52 

62 

51 

5866 

872 

7 

53 

62 

51 

9.5950 

880 

7 

54 

62 

51 

9.  6031 

888 

8 

55 

62 

50 

6111 

896 

8 

56 

62 

50 

6189 

904 

8 

57 

62 

49 

6266 

912 

8 

58 

61 

49 

6341 

919 

8 

59 

61 

49 

6416 

927 

8 

60 

8.509  7261 

8.512  6748 

9.6489 

0.934 

5.  6128 

6.534 

GEOGEAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  1°. 


197 


Lat. 

log  A 

logB 

logC 

logD 

logE 

logF 

O    1 

1  00 

8.509  7261 

8.512  6748 

9.6489 

0.934 

5.  6128 

6.534 

1 

61 

48 

560 

941 

29 

2 

61 

47 

631 

948 

29 

3 

61 

47 

701 

955 

29 

4 

61 

46 

769 

962 

29 

05 

60 

46 

836 

969 

29 

6 

60 

45 

903 

975 

29 

7 

60 

45 

9.6968 

982 

29 

8 

60 

44 

9.  7032 

988 

30 

9 

60 

44 

096 

0.995 

30 

10 

8.  509  7260 

8.  512  6743 

9.7158 

1.001 

5.  6130 

11 

59 

43 

220 

007 

30 

12 

59 

42 

281 

013 

30 

13 

59 

42 

341 

019 

30 

14 

59 

41 

400 

025 

31 

15 

59 

41 

458 

031 

31 

16 

58 

40 

516 

037 

31 

17 

58 

39 

572 

042 

31 

18 

58 

39 

628 

048 

31 

19 

58 

38 

684 

053 

31 

20 

8.  509  7258 

8.  512  6738 

9.7738 

1.059 

5.  6132 

6.658 

21 

57 

37 

792 

064 

32 

22 

57 

36 

846 

070 

32 

23 

57 

36 

898 

075 

32 

24 

57 

35 

9.7950 

080 

32 

25 

57 

35 

9.8002 

085 

32 

26 

56 

34 

053 

090 

33 

27 

56 

33 

103 

095 

33 

28 

56 

33 

152 

100 

33 

29 

56 

32 

202 

105 

33 

30 

8.509  7256 

8.  512  6731 

9.8250 

1.110 

5.  6133 

31 

55 

31 

298 

115 

34 

32 

55 

30 

346 

119 

34 

33 

55 

29 

393 

124 

34 

34 

55 

29 

439 

129 

34 

35 

S4 

28 

485 

133 

34 

36 

54 

27 

531 

138 

35 

37            54 

26 

576 

142 

35 

38            54 

26 

620 

147 

35 

39            53 

25 

664 

151 

35 

40 

8.509  7253 

8.  512  6724 

9.8708 

1.156 

5.6136 

6.755 

41 

53 

23 

751 

160 

36 

42 

53 

23 

794 

164 

36 

43 

52 

22 

836 

168 

36 

44 

52 

21 

878 

173 

36 

45 

52 

20 

920 

177 

37 

46 

52 

20 

961 

181 

37 

47 

51 

19 

9.9002 

185 

37 

48 

51 

18 

042 

189 

37 

49            51 

17 

082 

193 

38 

50       8.  509  7251 

8.512  6716 

9.9122 

1.197 

5.6138 

51 

50 

16 

161 

201 

38 

52 

50 

15 

200 

205 

38 

53 

50 

14 

239 

209 

39 

54 

49 

13 

277 

212 

39 

55 

49 

12 

315 

216 

39 

56 

49 

11 

353 

220 

39 

57 

49 

10 

390 

224 

40 

58 

48 

10 

427 

227 

40 

59 

48 

09 

464 

231 

40 

60       8,  509  7248 

8.512  6708 

9.9500 

1.2347 

5.6140 

6.834 

i 

198 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  2°. 


Lat. 

log  A 

logB 

logC 

log  D 

log  E       log  F 

0     / 

2  00 

8.  509  7248 

8.512  6708 

5.95002 

1.  2347 

5.  6140       6.  834 

1 

47 

07 

5363 

383 

41 

2 

47 

06 

5721 

419 

41 

3 

47 

05 

6076 

454 

41 

4 

47 

04 

6428 

489 

41 

05 

46 

03 

6777 

524 

42 

6 

46 

02 

7123 

559 

42 

7 

46 

01 

7467 

593 

42 

8 

45 

6700 

7808 

627 

43 

9 

45 

6699 

8146 

661 

43 

10 

8.  509  7245 

8.  512  6698 

9.  98482 

1.  2694 

5.  6143 

11 

44 

97 

8815 

727 

43 

12 

44 

97 

9145 

760 

44 

13 

44 

96 

9473 

793 

44 

14 

43 

95 

9.  99799 

826 

44 

15 

43 

94 

0.00122 

858 

45 

16 

43 

93 

0443 

890 

45 

17 

42 

91 

0762 

922 

45 

18 

42 

90 

1078 

953 

45  ' 

19 

42 

89 

1392 

1.2984 

46 

20 

8.  509  7241 

8.  512  6688 

0.  01703 

1.  3015 

5.  6146       6.  901 

21 

41 

87 

2013 

046 

46 

22 

41 

86 

2320 

077 

47 

23 

40 

85 

2625 

107 

47 

24 

40 

84 

2928 

138 

47 

25 

40 

83 

3229 

168 

48 

26 

39 

82 

3528 

197 

48 

27 

39 

81 

3825 

227 

48 

28 

38 

80 

4119 

256 

49 

29 

38 

79 

4412 

285 

49 

30 

8.509  7238 

8.512  6678 

0.04703 

1.3314 

5.  6149 

31 

37 

76 

4992 

343 

50 

32 

37 

75 

5279 

372 

50 

33 

37 

74 

5564 

400 

50 

34 

36 

73 

5847 

428 

51 

35 

36 

72 

6129 

456 

51 

36 

35 

71 

6408 

484 

51 

37 

35 

70 

6686 

512 

52 

38 

35 

68 

6962 

539 

52 

39 

34 

67 

7237 

567 

52 

40 

8.  509  7234 

8.  512  6666 

0.  07509 

1.3594 

5.  6153       6.  959 

41 

33 

65 

7780 

621 

53 

42 

33 

64 

8050 

648 

53 

43 

33 

62 

8317 

674 

54 

44 

32 

61 

8583' 

701 

54 

45 

32 

60 

8848 

727 

54 

46 

31 

59 

9111 

753 

55 

47 

31 

58 

9372 

779 

55 

48 

31 

56 

9631 

805 

56 

49 

30 

55 

0.  09890 

831 

56 

1  .  "   50 

8.  509  7230 

8.  512  6654 

0.  10146 

1.3856 

5.6156 

51 

29 

52 

0401 

882 

57 

52 

29 

51 

0655 

907 

57 

53 

28 

50 

0907 

932 

57 

54 

28 

49 

1158 

957 

58 

55 

28 

47 

1407 

1.  3982 

58 

56 

27 

46 

1655 

1.4007 

59 

57 

27 

45 

1902 

031 

59 

58 

26 

43 

2147 

055 

59 

59 

26 

42 

2390 

080 

60 

60 

8.509  7225 

8.512  6641 

0.12633 

1.4104 

5.6160       7.010 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  3°. 


199 


Lat. 

log  A 

diff.  l^L-0.03 

logC 

logD 

logE 

logF 

o   / 
3  00 

8.509  7225 

8.  512  6641 

0.  12633 

1.4104 

5.  6160 

7.010 

1 

25 

39 

2874 

28 

61 

2 

24 

38 

3113 

52 

61 

3 

24 

37 

3352 

75 

61 

4 

24 

35 

3589 

1.4199 

62 

05 

23 

34 

3825 

1.  4222 

62 

6 

23 

33 

4059 

46 

62 

7 

22 

31 

4293 

69 

63 

8 

22 

30 

4525 

1.4292 

63 

9 

21 

28 

4756 

1.  4315 

64 

10 

8.509  7221 

8.512  6627 

0.  14985 

1.4338 

5.6164 

11 

20 

26 

5214 

60 

65 

12 

20 

24 

54ftl 

1.4383 

65 

13 

19 

23 

5667 

1.4405 

65 

14 

19 

21 

5892 

28 

66 

15 

18 

20 

6116 

50 

66 

16 

18 

18 

6338 

72 

67 

17 

17 

17 

6560 

1.4494 

67 

* 

18 

17 

15 

6780 

1.  4516 

68 

19 

16 

14 

6999 

38 

68 

20 

8.509  7216 

8.512  6612 

0.  17217 

1.4560 

5.  6168 

7.055 

21 

15 

11 

7434 

1.4581 

69 

22 

15 

09 

7650 

1.4603 

69 

23 

14 

08 

7665 

24 

70 

24 

14 

06 

8079 

45 

70- 

25 

13 

05 

8292 

66 

71 

26 

13 

03 

8504 

1.4687 

71 

27 

12 

02 

8715 

1.  4708 

72 

28 

12 

6600 

8925 

29 

72 

29 

11 

6599 

9133 

50 

72 

30 

8.509  7211 

8.  512  6597 

0.  19341 

1.  4770 

5.  6173 

31 

10 

96 

9548 

1.4791 

73 

32 

10 

94 

9754 

1.4811 

74 

33 

09 

92 

19959 

32 

74 

34 

09 

91 

20163 

52 

75 

35 

08 

89 

0366 

72 

75 

36 

08 

88 

0568 

1.4892 

76 

37 

07 

86 

0769 

1.  4912 

76 

38 

07 

84 

0969 

32 

77 

39 

06 

83 

1168 

52 

77 

40 

8.509  7206 

8.  512  6581 

0.  21367 

1.  4971 

5.  6178 

7.096 

41 

05 

80 

1564 

1.4991 

78 

42 

04 

78 

1761 

1.5011 

79 

43 

04 

76 

1956 

30 

79 

44 

03 

75 

2151 

49 

80 

45 

03 

73 

2345 

68 

80 

46 

02 

71 

2538 

1.5088 

81 

47 

02 

69 

2731 

1.  5107 

81 

48 

01 

68 

2922 

26 

81 

49 

01 

66 

3113 

45 

-   82 

50 

8.509  7200 

8.  512  6564 

0.23302 

1.  5163 

5.6182 

51 

7199 

63 

3491 

1.5182 

83 

52 

99 

61 

3680 

1.5201 

84 

53 

98 

59 

3867 

19 

84 

54 

98 

58 

4053 

38 

85 

55 

97 

56 

4239 

56 

85 

56 

96 

54 

4424 

'  75 

86 

57 

96 

52 

4608 

1.5293 

86 

58 

95 

50 

4792 

1.  5311 

87 

59 

95 

49 

4974 

29 

87 

60 

8.509  7194 

8.  512  6547 

0.  25156 

1.5347 

5.6188 

7.133 

200 


GEOGRAPHIC    TABLES    AND    FOKMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  4°. 


Lat. 

log  A 

logB  ' 
diff.l"=-0.04 

logC 

logD 

log  E     log  F 

o   / 
4  00 

8.  509  7194 

8.512  6547 

0.  25156 

1.5347 

5.  6188     7.  133 

1 

93 

45 

5337 

65 

88 

2 

93 

43 

5518 

1.5383 

89 

3 

92 

42 

5697 

1.5401 

89 

4 

92 

40 

5876 

18 

90 

05 

91 

38 

6055 

36 

90 

6 

91 

36 

6232 

54 

91 

7 

90 

34 

6409 

71 

91 

8 

89 

32 

6585 

1.5489 

92 

9 

89 

31 

6760 

1.5506 

92 

10 

8.  509  7188 

8.512  6529 

0.  26935 

1.  5523 

5.  6193 

11 

87 

27. 

7109 

40 

93 

12 

87 

25* 

7282 

58 

94 

13 

86 

23 

7455 

75 

95 

14 

86 

21 

7627 

1.  5592 

95 

15 

85 

19 

7798 

1.  5609 

96 

16 

84 

17 

7968 

25 

96 

17 

84 

16 

8138 

42 

97 

18 

83 

14 

8308 

59 

97 

.19 

82 

12 

8476 

76 

98 

20 

8.509  7182 

8.  512  6510 

0.28644 

1.5692 

5.  6199     7.  168 

21 

81 

08 

8812 

1.  5709 

5.  6199 

22 

80 

06 

8978 

25 

5.6200 

23 

80 

04 

9144 

42 

00 

24 

79 

02 

9310 

58 

01 

25 

78 

6500 

9475 

74 

01 

26 

78 

6498 

9639 

1.  5791 

02 

27 

77 

96 

9802 

1.5807 

03 

28 

76 

94 

0.  29965 

23 

03 

29 

76 

92 

0.  30128 

39 

04 

30 

8.  509  7175 

8.612  6490 

0.  80290 

1.5855 

5.6204 

31 

74 

88 

0451 

71 

05 

32 

74 

86 

0611 

1.5887 

05- 

33 

73 

84 

0771 

1.5902 

06 

34 

72 

82 

0931 

18 

07 

35 

72 

80 

1090 

34 

07 

36 

71 

78 

1248 

50 

08 

37 

70 

76 

1406 

65 

08 

38 

70 

74 

1563 

81 

09 

39 

69 

72 

1719 

1.5996 

10 

40 

8.  509  7163 

8.512  6470 

0.  31875 

1.6011 

5.  6210     7.  200 

41 

67 

68 

2031 

27 

11 

42 

67 

65 

2186 

42 

12 

43 

66 

63 

2340 

57 

12 

44 

66 

61 

2494 

73 

13 

45 

65 

59 

2647 

1.6088 

13 

46 

64 

57 

2800 

1.  6103 

14 

47 

63 

55 

2953 

18 

15 

48 

63 

53 

3104 

33 

15 

49 

62 

51 

3255 

48 

16 

50 

8.509  7161 

8.512  6448 

0.33406 

1.  6163 

5.  6216 

51 

60 

•  46 

3556 

77 

17 

52 

60 

44 

3706 

1.6192 

18 

53 

59 

42 

3855 

1.  6207 

18 

54 

58 

40 

4004 

21 

19 

55 

57 

38 

4152 

36 

20 

56 

57 

35 

4300 

51 

20 

57 

56 

33 

4447 

65 

21 

58 

55 

31 

4594 

80 

22 

59 

55 

29 

4740 

1.6294 

22 

60 

8.509  7154 

8.  512  6427 

0.34885 

1.6308 

5.6223     7.229 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  5°. 


201 


Lat. 

log  A 

logB 
diff.  1"=-0.04 

logC 

logD 
diff.  1"=+0.22 

log  E.      log  F 

o   / 
5  00 

8.  509  7154 

8.5126427 

0.  34885 

T.  6308 

•  5.6223      f.229 

1 

53 

24 

5030 

23 

24 

o 

53 

22 

5175 

37 

24 

3 

52 

20 

5320 

51 

25 

4 

51 

18 

5464 

65 

26 

05 

50 

15 

5607 

79 

2fi 

6 

49 

13 

5750 

1.  6393 

27 

7 

49 

11 

5892 

1.6407 

•   28 

8            48 

08 

6034 

21 

28 

9            47 

06 

6176 

35 

29 

10       8.509  7146 

8.  512  6404 

0.  36317 

1.  6449 

5.  6230 

11            46 

6402 

6457 

63 

30 

12            45 

6399 

6597 

77 

31 

13 

44 

97 

6737 

1.  6491 

32 

14 

43 

95 

6876 

1.6504 

32 

15 

43 

92 

7015 

18 

33 

16 

42 

90 

7154 

32 

34 

17 

41 

88 

7292 

45 

34 

18            40 

85 

7429 

59 

35 

19            39 

83 

7566 

72 

36 

20       8.509  7139 

8.  512  6381 

0.  37703 

1.6586 

5.6236      7.256 

21            38 

78 

7839 

1.6599 

37 

22            37 

76 

7975 

1.6612 

38 

23 

36 

73 

8111 

26 

38 

24 

35 

71 

8246 

39 

-   39 

25 

35 

69 

8380 

52 

40 

26 

34 

66 

8514 

65 

41 

27 

33 

64 

8648 

78 

41 

28 

32 

61 

8781 

1.  6692 

42 

29 

31 

59 

8914 

1.6705 

43 

30 

8.  509  7131 

8.512  6356 

0.39047 

1.6718 

5.  6243 

31 

30 

54 

9179 

31 

44 

32 

29 

52 

9311 

44 

45 

33 

28 

49 

9442 

56 

46 

34 

27 

47 

9573 

69 

46 

35 

27 

44 

9704 

82 

47 

36 

26 

42 

9834 

1.6795 

48 

37 

26 

39 

0.  39964 

1.6808 

48 

38 

24 

37 

0.40094 

20 

49 

39 

23 

34 

0223 

33 

50 

40       8.509  7122 

8.  512  6332 

0.40351 

1  1.6846 

5.  6251      7.  282 

41            21 

29 

0480 

58 

51 

42 

21 

27 

0608 

71 

52 

43 

20 

24 

0735 

83 

53 

44 

19 

21 

0863 

1.6896 

54 

45 

18 

19 

0990 

1.6908 

54 

46 

17 

16 

1116 

21 

55 

47 

16 

14 

1242 

33 

56 

48 

16 

11 

1368 

45 

57 

49 

15 

09 

1493 

58 

57 

50 

8.509  7114 

8.512  6306 

0.  41619 

1.  6970 

5.  6258 

51 

13 

03 

1743 

82 

59 

52 

12 

6301 

1868 

1.6994 

60 

53 

11 

6298 

1992 

1.7006 

60 

54 

10 

96 

2115 

19 

61 

55 

09 

93 

2239 

31 

62 

56 

09 

90 

2362 

43 

63 

57 

08 

88 

2484 

55 

63 

58 

07 

85 

2607 

67 

64 

59 

06 

82 

2729 

79 

65 

60 

8.  509  7105 

8.  512  6280 

0.  42850 

1.7090 

5.  6266      7.  306 

202 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  6°. 


Lat. 

log  A 
diff.l"=-0.02 

logB 
diff.l"=-0.05 

logC 

logD 
diff.l"=+0.18 

logE 

logF 

0    / 

6  00 

8.  509  7105 

8.  512  6280 

0.42850 

1.7090 

5.  6266 

7.806 

1 

04 

77 

2972 

7102 

67 

2 

03 

74 

3093 

14 

67 

3 

02 

72 

3213 

26 

68 

4 

01 

69 

3334 

38 

69 

05 

01 

66 

3454 

50 

70 

6 

7100 

64 

3573 

61 

70 

7 

7099 

61 

3693 

73 

71 

8 

98 

58 

3812 

85 

72 

9 

97 

55 

3931 

1.7196 

73 

10 

8.  509  7096 

8.512  6253 

0.  44049 

1.7208 

5.  6274 

11 

95 

50 

4167 

19 

74 

12 

94 

47 

4285 

31 

75 

13 

93 

44 

4402 

42 

76 

14 

92 

42 

4519 

54 

77 

15 

91 

39 

4636 

65 

78 

16 

91 

36 

4753 

76 

78 

17 

90 

33 

4869 

88 

79 

18 

89 

31 

4985 

1.7299 

80 

19 

88 

28 

5101 

1.7310 

81 

20 

8.  509  7087 

8.  512  6225 

0.  45216 

1.  7322 

5.  6282 

7.329 

21 

86 

22 

5331 

33 

83 

22 

85 

19 

5446 

44 

83 

23 

84 

16 

5560 

55 

84 

24 

83 

14 

5674 

66 

85 

25 

82 

11 

5788 

78 

86 

26 

81 

08 

5902 

1.  7389 

87 

27 

80 

05 

6015 

1.7400 

88 

28 

79 

6202 

6128 

11 

88 

29 

78 

6199 

6241 

22 

89 

30 

8.  509  7077 

8.512  6196 

0.  46353 

1.  7433 

5.6290 

31 

76 

94 

6465 

44 

91 

32 

75 

91 

6577 

54 

92 

33 

74 

88 

6689 

65 

93 

34 

73 

85 

6800 

76 

93 

35 

72 

82 

6911 

87 

94 

36 

71 

79 

7022 

1.7498 

95 

37 

70 

76 

7132 

1.7508 

96 

38 

70 

73 

7242 

19 

97 

39 

69 

70 

7352 

30 

98 

40 

8.  509  7068 

8.  512  6167 

0.  47462 

1.7541 

5.6299 

7.351 

41 

67 

64 

7571 

51 

5.6299 

42 

66 

61 

7681 

62 

5.6300 

43 

65 

58 

7789 

73 

01 

44 

64 

55 

7898 

83 

02 

45 

63 

52 

8006 

1.  7594 

03 

46 

62 

49 

8114 

1.  7604 

04 

47 

61 

46 

8222 

15 

05 

48 

60 

43 

8330 

25 

06 

49 

59 

40 

8437 

36 

06 

50 

8.509  7058 

8.512  6137 

0.48544 

1.  7646 

5.6207 

51 

57 

34 

8651 

56 

08 

52 

56 

31 

8757 

67 

09 

53 

55 

28  - 

8864 

77 

10 

54 

53 

25 

8970 

87 

11 

55 

52 

22 

9075 

1.7698 

12 

56 

51 

19 

9181 

1.7708 

13 

57 

50 

16 

9286 

18 

13 

58 

49 

13 

9391 

28 

14 

59 

48 

10 

9496 

38 

15 

60 

8.  509  7047 

8.512  6107 

0.49600 

1.7749 

5.  6216 

7.371 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations— Continned. 

LATITUDE  7°. 


203 


Lat. 

log  A 
diff.l"=-0.02 

logB 
diff.l"=-0.06 

logC 

logD 
diff.l"=+0.16 

logE 

logF 

O    1 

7  00       8.  509  7047 

8.  512  6107 

0.49600 

I.  7749 

5.6316 

7.371 

1 

46 

03 

705 

59 

17 

2 

45 

6100 

809 

69 

18 

3 

44 

6097 

0.49913 

79 

19 

4 

43 

94 

0.  50016 

89 

20 

05 

42 

91 

119 

1.  7799 

21 

6 

41 

88 

222 

1.  7809 

22 

7 

40 

85 

325 

19 

23 

8 

39 

82 

428 

29 

23 

9 

38 

78 

530 

•  39 

24 

10 

8.509  7037 

8.  512  6075 

0.50632 

1.7849 

5.6325 

11 

36 

72   - 

734 

59 

26 

12 

35 

69 

836 

68 

27 

13 

34 

66 

0.50937 

78 

28 

14 

33 

62 

0.  51039 

88 

29 

15 

32 

59 

140 

1.  7898 

30 

16 

30 

56 

240 

1.7908 

31 

17 

29 

53 

341 

17 

32 

18            28 

50 

441 

27 

33 

19    !         27 

46 

541 

37 

34 

20       8.509  7026 

8.512  6043 

0.  51641 

1.7946 

5.6335 

7.391 

21            25 

40 

741 

56 

36 

22            24 

37 

840 

66 

37 

23 

23 

33 

0.  51939 

75 

37 

24 

22 

30 

0.  52038 

85 

38 

25 

21 

27 

137 

1.7994 

39 

26 

20 

23 

236 

1.8004 

40 

27 

19 

20 

334 

13 

41 

28 

17 

17 

432 

23 

42 

29 

16 

14 

530 

32 

43 

30 

8.509  7015 

8.  512  6010 

0.  52628 

1.8042 

5.6344 

31 

14 

07 

725 

51 

45 

32 

13 

04 

822 

61 

46 

38 

12 

6000 

0.  52919 

70 

47 

34 

11 

5997 

0.  53016 

79 

48 

35 

10 

94 

113 

89 

49 

36 

09 

90 

209 

1.8098 

50 

37 

07 

87 

306 

1.8107 

-  51 

38 

06 

83 

402 

17 

52 

39 

05 

80 

497 

26 

53 

40 

8.509  7004 

8.  512  5977 

0.  53593 

1.8135 

5.6354 

7.409 

41 

03 

73 

688 

44 

55 

42 

02 

70 

784 

53 

56 

43 

01 

66 

879 

63 

57 

44 

7000 

63 

0.  53973 

72 

58 

45 

6998 

60 

0.  54068 

81 

59 

46 

97 

56 

162 

90 

60 

47 

96 

53 

257 

1.8199 

61 

48 

95 

49 

351 

1.  8208 

62 

49 

94 

46 

444 

17 

63 

50 

8.  509  6993 

8.  512  5942 

0.  54538 

1.8226 

5.  6364 

51 

91 

39 

631 

35 

65 

52 

90 

35 

725 

44  . 

66 

53 

89 

32 

818 

53. 

67 

54 

88 

28 

0.54911 

62 

68 

55 

87 

25 

0.55003 

71 

69 

56 

86 

21 

096 

80 

70 

57 

84 

18 

188 

89 

71 

• 

58 

83 

14 

280 

1.8298 

72 

59 

82 

11 

372 

1.8307 

73 

60 

8.509  6981 

8.  512  5907 

0.  55464 

*   1.8315 

5.  6374 

7.427 

204 


GEOGRAPHIC    TABLES    ANT)    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  8°. 


Lat. 

log  A 
diff.  1"=-0.02 

logB 
diff.  1"=-0.06 

logC 

logD 
diff.  1"=+0.14 

log  E 
diff.  1"=+0.02 

logF 

o   / 
8  00 

8.  509  6981 

8.  512  5907 

0.  55464 

1.  8315 

5.  6374 

7.427 

1 

80 

04 

556 

24 

75 

2 

79 

5900 

646 

33 

76 

3 

77 

5897 

738 

42 

77 

4 

76 

93 

829 

50 

78 

05 

75 

90 

0.  55919 

59 

79 

6 

74 

86 

0.  56010 

68 

80 

7 

73 

82 

100 

77 

81 

8 

71 

79 

191 

85 

82 

9 

70 

75 

281 

1.8394 

83 

10 

8.  509  6969 

8.  512  5872 

0.  56371 

1.8403 

5.6384 

11 

68 

68 

460 

12 

85 

12 

67 

64 

550 

20 

86 

13 

65 

61 

639 

28 

87 

14 

64 

57 

728 

37 

88 

15 

63 

54 

817 

45 

90 

16 

62 

50 

906 

54 

91 

17 

61 

46 

0.  56995 

62 

92 

18 

59 

43 

0.  57083 

71 

93 

19 

58 

39 

172 

79 

94 

20 

8.  509  6957 

8.  512  5835 

0.57260 

1.8488 

5.  6395 

7.444 

21 

56 

3-2 

348 

1.8496 

96 

22 

54 

28 

436 

1.8605 

97 

23 

53 

24 

523 

13 

98 

24 

52 

20 

611 

21 

99 

25 

51 

17 

698 

30 

5.6400 

26 

49 

13 

785 

38 

5.  6401 

27 

48 

09 

872 

46 

02 

28 

47 

06 

0.  57959 

55 

03 

29 

46 

5802 

0.  58045 

63 

04 

30 

8.509  6945 

8.  512  5798 

0.58132 

1.  8571 

5.6406 

31 

43 

94 

218 

80 

07 

32 

42 

91 

304 

88 

08 

33 

41 

87 

390 

1.8596 

09 

34 

•   39 

83 

476 

1.  8604 

10 

35 

38 

79 

562 

13 

11 

36 

37 

75 

647 

21 

12 

37 

36 

72 

732 

29 

13 

38 

34 

68 

818 

37 

14 

39 

33 

64 

903 

•    45 

15 

40 

8.509  6932 

8.512  5760 

0.  58987 

1.8653 

5.  6416 

7.461 

41 

31 

56 

0.  59072 

61 

18 

42 

29 

53 

157 

69 

19 

43 

28 

49 

241 

77 

20 

44 

27 

45 

325 

85 

21 

45 

25 

41 

409 

1.8693 

22 

46 

24 

37 

493 

1.8701 

23 

47 

23 

33 

577 

09 

24 

48 

22 

29 

660 

17 

25 

49 

20 

26 

744 

25 

26 

50 

8.509  6919 

8.  512  5722 

0.  59827 

1.8733 

5.  6428 

51 

18 

18 

910 

41 

29 

52 

16 

14 

0.  59993 

49 

30 

53 

15 

10 

0.  60076 

57 

31 

54 

14 

06 

159 

65 

32 

55 

12 

5702 

241 

73 

33 

56 

11 

569S 

324 

81 

34 

57  ' 

10 

94 

406 

89 

36 

58 

09 

90 

488 

1.8796 

37 

59 

07 

86 

670 

1.8804 

38 

60 

8.509  6906 

8.512  5682 

0.60652 

1.8812 

5.  6439 

7.476 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  9°. 


205 


Lat. 

log  A 
diff.l"=-0.02 

logB 
diff.l"=-0.07 

logC 

logD 
diff.l"=+0.12 

logE 
diff.l"=+0.02 

logF 

o   / 

9  00 

8.509  6906 

8.  512  5682 

0.60652 

1.8812 

o.  6439 

7.476 

1           05 

78 

733 

20 

40 

2           03 

74 

815 

27 

41 

3 

02 

70 

896 

35 

42 

4 

6901 

66 

0.60977 

43 

44 

05 

6899 

62 

0.  61058 

51 

45 

6 

98 

58 

139 

58 

46 

7 

97 

54 

220 

66 

47 

8 

95 

50 

301 

74 

48 

9 

94 

46 

881 

81 

49 

10 

8.  509  6893 

8.  512  5642 

0.61461 

1.8889 

5.6450 

11 

91 

38 

542 

1.8897 

52 

12 

90 

34 

622 

1.8904 

53 

13 

89 

30 

702 

12 

54 

14 

87 

26 

781 

19 

55 

15 

86 

22 

861 

27 

56 

16 

84 

18 

0.  61941 

34 

57 

17 

83 

14 

0.  62020 

42 

59 

18 

82 

10 

099 

50 

60 

19 

80 

06 

178 

57 

61 

20 

8.  509  6879 

8.  512  5602 

0.  62257 

1.8964 

5.6462 

7.490 

21 

78 

5598 

336 

72 

63 

22 

76 

93 

415 

79 

65 

23 

75 

89 

493 

87 

66 

24 

74 

85 

572 

1.8994 

67 

25 

72 

81 

650 

1.9002 

68 

26 

71 

77 

728 

09 

69 

27 

69 

73 

806 

17 

70 

28 

68 

69 

884 

24 

72 

29           67 

64 

0.  62962 

31 

73 

30 

8.  509  6865 

8.512  5560 

0.  63039 

1.9039 

5.  6474 

31 

64 

56 

117 

46 

75 

32           62 

52 

194 

53 

76 

33           61 

48 

271 

61 

'   78 

34 

60 

43 

349 

68 

79 

86 

58 

39 

426 

75 

80 

36 

57 

35 

502 

82 

81 

37 

55 

31 

579 

90 

83 

38 

54 

27 

656 

1.9097 

84 

39 

53 

22 

732 

1.  9104 

85 

40 

8.509  6851 

8.  512  5518 

0.  63808 

1.9111 

5.  6486 

7.505 

41 

50 

14 

885 

19 

87 

42 

48 

10 

0.63961 

26 

89 

43 

47 

05 

0.64037 

33 

90 

44 

45 

5501 

112 

40 

91 

45 

44 

5497 

188 

47 

92 

46 

43 

92 

264 

54 

94 

47 

41 

88 

339 

61 

95 

48 

40 

84 

415 

69 

96 

49 

38 

80 

490 

76 

97 

50 

8.509  6837 

8.  512  5475 

0.  64565 

1.9183 

5.  6498 

51 

35 

71 

640 

90 

5.6500 

52 

34 

67 

'  715 

1.  9197 

01 

53 

33 

62 

789 

1.9204 

02 

54 

31 

58 

864 

11 

03 

55 

30 

54 

0.  64938 

18 

05 

56 

28 

49 

0.  65013 

25 

06 

57 

27 

45 

087 

32 

07 

58 

25 

40 

161 

39 

08 

59 

24 

36 

235 

46 

10 

60 

8.  509  6822 

8.  512  5432 

0.65309 

1.9253 

5.6411 

7.518 

206 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  10°. 


Lat. 

log  A 
diff.l"=-0.0; 

logB 
!  diff.l"=-0.08 

logC 

logD 
diff.l"=+0.11 

16gE 
diff.  1"=+0.02 

logF 

o   / 
10  00 

8.  509  6822 

8.  512  5432 

0.  65309 

I.  9253 

5.  6511 

7.518 

1 

21 

27 

383 

60 

12 

2 

19 

23 

456 

67 

13 

3 

18 

19 

530 

74 

15 

4 

17 

14 

603 

80 

16 

05 

15 

10 

677 

87 

17 

6 

14 

05 

750 

1.  9294 

18 

7 

12 

5401 

823 

1.9301 

20 

8 

11 

5396 

896 

08 

21 

9 

9 

92 

0.  65968 

15 

22 

10 

8.  509  6808 

8.  512  5388 

0.  66041 

1.9322 

5.  6524 

11 

06 

83 

114 

28 

25 

12 

05 

79 

186 

35 

26 

13 

03 

74 

259 

42 

27 

14 

02 

70 

331 

49 

29 

15 

6800 

65 

403 

56 

30 

16 

6799 

61 

475 

62 

31 

17 

97 

56 

547 

69 

33 

.  18 

96 

52 

619 

76 

34 

19 

94 

47 

691 

82 

35 

20 

8.  509  6793 

8.512  5343  . 

0.  66762 

1.  9389 

5.6536 

7.532 

21 

91 

38 

834 

1.9396 

38 

22 

90 

33 

905 

1.9403 

39 

23 

88 

29 

0.  66976 

09 

40 

24 

87 

24 

0.  67047 

16 

42 

25 

85 

20 

118 

23 

43 

26 

84 

15 

189 

29 

44 

27 

82 

11 

260 

36 

46 

28 

81 

06 

331 

42 

47 

29 

79 

5302 

401 

49 

48 

30 

8.509  6777 

8.512  5297 

0.  67472 

1.9456 

5.6549 

31 

76 

92 

542 

62 

51 

32 

74 

88 

613 

69 

52 

33 

73 

83 

683 

75 

53 

34 

71 

79 

753 

82 

55 

35 

70 

74 

823 

88 

56 

36 

68 

69 

893 

1.9495 

57 

37 

67 

65 

0.  67962 

1.9501 

59 

38 

65 

60 

0.  68032 

08 

60 

39 

64 

55 

102 

14 

61 

40 

8.509  6762 

8.  512  5251 

0.  68171 

1.9521 

5.6563 

7.544 

41 

60 

46 

240 

27 

64 

42 

59 

41 

310 

34 

65 

43 

57 

37 

379 

40 

67 

44 

56 

32 

448 

47 

68 

45 

54 

27 

517 

53 

69 

46 

53 

23 

586 

60 

71 

47 

51 

18 

654 

66 

72 

48 

50 

13 

723 

72 

73 

49 

48 

08 

791 

79 

75 

50 

8.  509  6746 

8.512  5204 

0.  68860 

1.9585 

5.6576 

51 

45 

5199 

928 

91 

78 

52 

43 

94 

0.  68996 

1.  9598 

79 

53 

42 

89 

0.  69064 

1.9604 

80 

54 

40 

85 

132 

10 

82 

55 

38 

80 

200 

17 

83. 

56 

37 

75 

268 

23 

84 

57 

35 

70 

336 

29 

86 

58 

34 

66 

404 

36 

87 

59 

32 

61 

471 

42 

88 

60 

8.  509  6730 

8.  512  5156 

0.  69539 

1.9648 

5.6590 

7.556 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  11°. 


207 


Lat. 

log  A 
diff.l"=-0.03 

logB 
diff.l"=-0.08 

logC 

logD 
diff.l"=+0.10 

logE 
diff.l"=+0.02 

logF 

o   / 

11  00       8.509  6730 

8.  512  5156 

0.  69539 

1.9648 

5.  6590 

7.556 

1 

29 

51 

606 

54 

91 

2 

27 

46 

673 

61 

93 

3 

26 

41 

740 

67 

94 

4 

24 

37 

807 

73 

95 

05 

22 

32 

874 

7.9 

97 

6 

21 

27 

0.69941 

86 

98 

7            19 

22 

0.70008 

92 

5.  6599 

8 

18 

17 

074 

1.9698 

5.6601 

9            16 

12 

141 

1.9704 

02 

10       8.509  6714 

.   8.512  5108 

0.  70208 

1.  9710 

5.  6604 

11            13 

5103 

274 

16 

05 

12            11 

5098 

340 

23 

06 

13            09 

5093 

406 

29 

08 

14            08 

88 

473 

35 

09 

15            06 

83 

539" 

41 

11 

16            05 

78 

604 

47 

12 

17            03 

73 

670 

53 

13 

18            01 

68 

736 

59 

15 

19           6700 

•  63 

802 

65 

16 

20       8.5096698 

8.512  5058 

0.  70867 

1.9771 

5.6618 

7.568 

21            96 

53 

933 

77 

19 

22            95 

49 

0.70998 

83 

20 

23            93 

44 

0.71063 

89 

22 

24            91 

39 

128 

1.9795 

23 

25             90 

34 

194 

1.9801 

25 

26            88 

29 

259 

07 

26 

27            86 

24 

323 

13 

27 

28            85 

19 

388 

19 

29 

29            83 

14 

453 

25 

30 

30       8.5096681 

8.512  5009 

0.  71518 

1.9831 

5.  6632 

31             80 

04 

582 

37 

33 

32            78 

4999 

647 

43 

35 

33 

76 

94 

711 

49 

36 

34 

75 

89 

775 

55 

37 

35 

73 

83 

840 

61 

39 

36 

71" 

78 

904 

67 

40 

37 

70 

73 

0.  71968 

73 

42 

•  38 

68 

68 

0.  72032 

79 

43 

39 

66 

63 

095 

85 

45 

40 

8.  -309  6665 

8.5124958 

0.72159 

1.9890 

5.6646 

7.580 

41 

63 

53 

223 

1.9896 

47 

42 

61 

48 

286 

1.9902 

49 

43 

59 

43 

350 

08 

50 

44 

58 

38 

413 

14 

52 

45 

56 

33 

477 

20 

53 

46 

54 

28 

540 

25 

55 

47 

53 

22 

603 

31 

56 

48 

51 

17 

666 

37 

58 

49 

49 

12 

729 

43 

59 

50 

8.  509  6647 

8.  512  4907 

0.  72792 

1.9949 

5.6661 

51 

46 

4902 

855 

54 

62 

52 

44 

4897 

918 

60 

64 

53 

43 

92 

0.  72980 

66 

65 

54 

41 

86 

0.  73043 

72 

66 

55 

39 

'81 

106 

77 

68 

56 

37 

76 

168 

83 

69 

57 

35 

71 

230 

89 

71 

58 

34 

66 

293 

94 

72 

59 

32 

60 

355 

1.9900 

74 

60 

8.509  6630 

8.512  4855 

0.  73417 

2.0006 

5.  6675 

7.591 

208 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  12°. 


Lat. 

log  A 
diff.l"=-0.03 

logB 
diff.l"=-0.09 

logC 

logD 
diff  .  1"=  +0.09 

log  E 
diff.  1"--  +0.04 

logF 

o   / 

12  00 

8.  509  6630 

8.512  4855 

0.  73417 

2.0006 

5.6675 

7.591 

1 

29 

50 

479 

11 

77 

2 

27 

45 

541 

17 

78 

3 

25 

39 

603 

23 

80 

4 

23 

34 

664 

28 

81 

05 

21 

29 

726 

34 

83 

6 

20 

24 

788 

40 

84 

7 

18 

18 

849 

45 

86 

8 

16 

13 

911 

51 

87 

9 

14 

08 

0.  73972 

57 

89 

10 

18.509  6613 

8.512  4803 

0.  74033 

2.0062 

5.6690 

11 

11 

4797 

094 

67 

92 

12 

09 

92 

156 

73 

93 

13 

07 

87 

217 

79 

95 

14 

06 

81 

278 

84 

96 

15 

04 

76 

339 

90 

98 

16 

02 

71 

399 

2.0096 

99 

17 

6600 

65 

460 

2.  0101 

5.  6701 

18 

6599 

60 

521 

07 

02 

19 

97 

55 

581 

12 

04 

20 

8.  509  6595 

8.  512  4749 

0.  74642 

2.  0118 

5.  6705 

7.601 

21 

93 

44 

702 

23 

07 

22 

91 

39 

763 

29 

08 

23 

90 

33 

823 

34 

10 

24 

88 

28 

883 

40 

11 

25 

86 

23 

0.  74943 

45 

13 

26 

84 

17 

0.  75003 

50 

14 

27 

82 

12 

063 

56 

16 

28 

81 

06 

123 

61 

17 

29 

79 

4701 

183 

67 

19 

30 

8.  509  6577 

8  512  4696 

0.  75243 

2.  0172 

5.  6720 

31 

75 

90 

302 

77 

22 

32 

73 

85 

362 

83 

24 

33 

72 

79 

422 

88 

25 

34 

70 

74 

481 

94 

27 

35 

08 

68 

540 

2.  0199 

28 

36 

66 

63 

600 

2.  0205 

30 

37 

64 

57 

659 

10 

31 

38 

62 

62 

718 

15 

33 

39 

61 

46 

111 

21 

34 

40 

8.  509  6559 

8.  512  4641 

0.  75836 

2.  0226 

5.  6736 

7.  611 

41 

57 

35 

895 

32 

37 

42 

55 

30 

0.  75954 

37 

39 

43 

53 

24 

0.  76013 

42 

41 

44 

51 

19 

072 

47 

42 

45 

50 

13 

130 

53 

44 

46 

48 

08 

189 

58 

45 

47 

46 

4602 

247 

63 

47 

48 

44 

4597 

306 

69 

48 

49 

42 

91 

364 

74 

50 

50 

8.  509  6540 

8.  512  4586 

0.76422 

2.  0279 

5.6751 

51 

39 

80 

481 

84 

53 

52 

37 

75 

539 

90 

55 

53 

35 

69 

597 

2.0295 

56 

54 

33 

63 

655 

2.0300 

58 

55 

31 

58 

713 

05 

59 

56 

29 

52 

771 

10 

61 

57 

27 

47 

828 

16 

62 

58 

25 

41 

886 

21 

64 

59 

24 

35 

0.  76944 

26 

66 

60 

8.  509  6522 

8.  512  4530 

0.  77001 

2.0331 

5.  6767 

7.621 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  13°. 


209 


Lat. 

log  A 
diff.  1"=-0.03 

logB 
diff.  1"=-0.10 

logC 
diff.  1"=+0.93 

logD 
diff.  1"=+0.08 

logE 
diff.  1"  =  +  0.03 

logF 

o   / 
13  00 

8.509  6522 

8.  512  4530 

0.  77001 

2.0331 

5.6767 

7.  621 

1 

20 

24 

059 

36 

69 

2 

18 

19 

116 

42 

70 

3 

16 

13 

174 

47 

72 

4 

14 

07 

231 

52 

74 

05 

12 

4502 

288 

57 

75 

6 

10 

4496 

346 

62 

77 

7 

09 

90 

403 

67 

78 

8 

07 

85 

460 

73 

80 

1 

05 

79 

517 

78 

82 

10 

8.509  6503 

8.  512  4473 

0.  77574 

2.0383 

5.6783 

11 

6501 

67 

630 

88 

85 

12 

6499 

62 

687 

93 

86 

13 

97 

56 

744 

2.  0398 

88 

14 

95 

50 

801 

•2.  0403 

90 

15 

93 

45 

857 

08 

91 

16 

91 

39 

914 

13 

93 

17 

90 

33 

,  0.  77970 

18 

94 

18 

88 

27 

0.78027 

23 

96 

19 

86  • 

22 

083 

28 

98 

20 

8.509  6484 

8.  512  4416 

0.  78139 

2.0433 

5.6799 

7.631 

21 

82 

10 

195 

38 

5.6801 

22 

80 

4404 

251 

44 

03 

23 

78 

4399 

307 

49 

04 

24 

76 

93 

363 

54 

06 

25 

74 

87 

419 

59 

07 

26 

72 

81 

475 

64 

09 

27 

70 

76 

531 

69 

11 

28 

68 

70 

B87 

74 

12 

29 

66 

64 

642 

78 

14 

30 

8.509  6464 

8.  512  4358 

0.  78698 

2.0483 

5.  6816 

31 

63 

52 

754 

88 

17 

32 

61 

46 

809 

93 

19 

33 

59 

41 

865 

2.0498 

20 

34 

57 

35 

920 

2.0503 

22 

35 

55 

29 

0.  78975 

08 

24 

36 

53 

23 

0.  79030 

13 

25 

37 

51 

17 

086 

18 

27 

38 

49 

11 

141 

23 

29 

39 

47 

4305 

196 

28 

30 

40 

8.  509  6445 

8.  512  4299 

0.  79251 

2.0533 

5.  6832 

7.640 

41 

43 

94 

306 

38 

34 

42 

41 

88 

360 

42 

35 

43 

39 

82 

415 

47 

37 

44 

37 

76 

470 

52 

39 

45 

35 

70 

525 

57 

40 

46 

33 

64 

579 

62 

.  42 

47 

31 

58 

634 

67 

44 

48 

29 

52 

588 

72 

45 

49 

27 

46 

743 

76 

47 

50 

8.  509  6425 

8.  512  4240 

0.  79797 

2.0581 

5.  6849 

51 

23 

34 

851 

86 

50 

52 

21 

28 

905 

91 

52 

53 

19 

22 

0.79960 

2.0596 

54 

54 

17 

16 

0.80014 

2.0601 

55 

55 

15 

10 

068 

05 

57 

56 

13 

4204 

122 

10 

59 

57 

11 

4198 

176 

15 

60 

58 

09 

92 

230 

20 

62 

x59 

07 

86 

284 

24 

64 

60 

8.  509  6405 

8.512  4180 

0.  80337 

2.0629 

5.  6865 

7.649 

46061—08 14 


210 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  14°. 


Lat, 

log  A 
diff.l"=-0.03 

logB 
diff.l"=-0.10 

logC 
diff.l"=+0.87 

logD 
diff.l"=+0.08 

logE 
diff.l"=+0.03 

logF 

0    / 

14  00 

8.  509  6405 

8.512  4180 

0.  80337 

2.  0629 

5.6865 

7.649 

1 

03 

74 

391 

34 

67 

2 

6401 

68  • 

445 

39 

69 

3 

6399 

62 

498 

43 

71 

4 

97 

56 

552 

48 

72 

05 

95 

50 

605 

53 

74 

6 

93 

44 

659 

58 

76 

7 

91 

38 

712 

62 

77 

8 

89 

32 

765 

67 

79 

9 

87 

26 

819 

72 

81 

10 

8.  509  6385 

8.512  4120 

0.  80872 

2.0676 

5.6882 

11 

83 

14 

925 

81 

84 

12 

81 

08 

0.  80978 

86 

86 

13 

79 

4101 

0.81031  ' 

90 

88 

14 

77 

4095 

084 

2.0695 

89 

15 

75 

89 

137 

2.  0700 

91 

16 

73 

83 

190 

04 

93 

17 

71 

77 

243  » 

09 

94 

18 

69 

71 

295 

14 

96 

19 

67 

65 

348 

18 

98 

20 

8.  509  6365 

8.512  4059 

0.  81401 

2.  0723 

5.6900 

7.658 

21- 

63 

52 

453 

28 

01 

22 

61 

46 

506 

32 

03 

23 

58 

40 

558 

36 

05 

24 

56 

34 

611 

41 

06 

25 

54 

28 

663 

46 

08 

26 

52 

21 

715 

51 

10 

27 

50 

15 

767 

55 

12 

28 

48 

09 

820 

60 

13 

29 

46 

4003 

872 

64 

15 

0 

30 

8.  509  6344 

8.512  3997 

0.81924 

2.  0769 

5.6917 

31 

42 

90 

0.81976 

73 

19 

32 

40 

84 

0.  82028 

78 

20 

33 

38 

78 

080 

83 

22 

34 

36 

72 

131 

87 

24 

35 

34 

65 

183 

92 

26 

36 

32 

59 

235 

2.  0796 

27 

37 

29 

53 

287 

2.  0801 

29 

38 

27 

47 

338 

05 

31 

39 

25 

40 

390 

10 

33 

40 

8.509  6323 

8.512  3934 

0.  82441 

2.  0814 

5.6934 

7.667 

41 

21 

28 

493 

19 

36 

42 

19 

22 

544 

23 

38 

43 

17 

15 

596 

28 

40 

44 

15 

09 

647 

32 

41 

45 

13 

3903 

698 

i        37 

43 

46 

11 

3896 

749 

41 

45 

47 

08 

90 

800 

46 

47 

48 

06 

84 

852 

50 

48 

49 

04 

77 

903 

54 

50 

50 

8.  509  6302 

8.  512  3871 

0.  82954 

2.  0859 

5.  6952 

51 

6300 

65 

0.  83005 

63 

54 

52 

6298 

58 

055 

68 

55 

53 

96 

52 

106 

72 

57 

54 

94 

45 

157 

77 

59 

55 

92 

39 

208 

81 

61 

56 

89 

33 

258 

85 

63 

57 

87 

26 

309 

90 

64 

58 

85 

20 

360 

94 

66 

59 

83 

13 

410 

2.  0899 

68 

60 

8.  509  6281 

8.512  3807 

0.83461 

2.0903 

5.6970 

7.675 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  15°. 


211 


Lat. 

log  A 
diff.l"=-0.04 

logB 
diff.l"  =  -0.11 

logC 
diff.l"=+0.82 

logD 
diff.l"=-+0.07 

logE 
diff.  l"=  +0.03 

logF 

o   / 

15  00 

8.  509  6281 

8.512  3807 

0.83461 

2.0903 

5.  6970 

7.675 

1 

79 

3801 

511 

07 

72 

a 

77 

3794 

561 

12 

73 

3 

74 

"88 

612 

16 

75 

4 

72 

81 

662 

21 

77 

05 

70 

75 

712 

25 

79 

6 

68 

68 

762 

29 

80 

7 

66 

62 

813 

34 

82 

8 

64 

56 

863 

38 

84 

g 

62 

49 

913 

42 

86 

10 

8.  509  6259 

8.512  3743 

0.83963 

2.0947 

5.6988 

11 

57 

36 

0.  84012 

51 

89 

12 

55 

30 

062 

55 

91 

13 

53 

23 

112 

59 

93 

14 

51 

17 

162 

64 

95 

15 

49 

10 

212 

68 

97 

16 

46 

3704 

261 

72 

5.  6999 

17 

44 

3697 

311 

77 

5.  7000 

18 

42 

91 

361 

81 

02 

19 

40 

84 

410 

85 

04 

20 

8.  509  6238 

8.  512  3677 

0.844CO. 

2.0990 

5.7006 

7.683 

21 

36 

71 

509 

94 

08 

22 

33 

64 

558 

2.0998 

09 

23 

31 

•58 

608 

2.1002 

11 

24 

29 

51 

667 

07 

13 

25 

27 

45 

706 

11 

15 

26 

24 

38 

755 

15 

17 

27 

22 

31 

804 

19 

19 

28 

20 

25 

854 

23 

20 

29 

18 

18 

903 

28 

22 

30 

8.  509  6216 

8.  512  3612 

0.  84952 

2.  1032 

5.7024 

31 

14 

3606 

0.85001 

36 

26 

32 

11 

3598 

049 

40 

28 

33 

09 

92 

098 

44 

30 

34 

07 

H 

147 

49 

31 

'35 

n:, 

79 

196 

53 

33 

36 

02 

72 

245 

57 

36 

37 

6200 

65 

293 

61 

37 

38 

6198 

59 

342 

65 

39 

39 

96 

52 

390 

69 

41 

40 

8.  509  6194 

8.  512  3545 

0.85439 

2.  1074 

5.  7042 

7.691 

41 

91 

39 

487 

78 

44 

42 

89 

32 

636 

82 

46 

43 

87 

25 

584 

86 

48 

44 

85 

19 

633 

90 

50 

45 

82 

12 

C81 

94 

52 

46 

80 

3505 

729 

2.1099 

64 

47 
48 

78 
76 

3498 
92 

111 
825 

2.noi 

55 

57 

49 

73 

85 

874 

11 

59 

50 

8.  509  6171 

8.  512  3478 

0.  85922 

2.1115 

5.7061 

51 

69 

71 

0.  85970 

19 

63 

52 

67 

65 

0.86018 

23 

65 

53 

64 

58 

066 

27 

67 

54 

62 

51 

113 

31 

69 

55 

60 

44 

161 

35 

70 

66 

58 

38 

209 

39 

72 

67 

55 

31 

257' 

44 

74 

68 

63 

24 

'  304 

48 

76 

59 

51 

17 

352 

52 

78 

60 

8.  o09  6149 

8.512  3411 

0.864QO 

2.1156 

5.7080 

7.698 

212 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. —  Geodetic  position  computations — Continued. 

LATITUDE  16°. 


Lat. 

log  A 
diff.l"=-0.04 

logB 
diff.l"=-0.12 

logC 

diff.l"=+0.77 

logD 
diff.l"=+0.06 

logE 
diff.l"=+0.03 

logF 

o   / 
16  00 

8.  509  6149 

8.  512  3411 

0.86400 

2.  1156 

5.7080 

7.698 

1 

46 

3404 

447 

60 

82 

2 

44 

3397 

495 

64 

84 

3 

42 

90 

542 

'  >  '68 

85 

4 

40 

83 

590 

72 

87 

05 

37 

76 

637 

76 

89 

6 

35 

70 

684 

80 

91 

7 

33 

63 

732 

84 

93 

8 

30 

56 

779 

88 

95 

9 

28 

49 

826 

92 

97 

10 

8.  509  6126 

8.512  3342 

0.  86873 

2.  1196 

5.7099 

11 

24 

35 

921 

2.  1200 

5.  7101 

12 

21 

28 

0.  86968 

04 

03 

13 

19 

22 

0.  87015 

08 

04 

14 

17 

15 

062 

12 

06 

15 

14 

08 

109 

16 

08 

16 

12 

3301  • 

156 

20 

10  . 

17 

10 

3294 

202 

24 

12 

18 

08 

87 

249 

28 

14 

19 

05 

80 

2% 

32 

16 

20 

8.  509  6103 

8.512  3273 

0.87343 

2.  1236 

5.7118 

7.705 

21 

6101 

66 

389 

40 

20 

2iJ 

6098 

59 

436 

44 

22 

23 

96 

52 

483 

47 

24 

24 

94 

45 

529 

51 

25 

25 

91 

39 

576 

55 

27 

26 

89 

32 

622 

59 

29 

27 

87 

25 

669 

63 

31 

28 

84 

18 

715 

67 

33 

29 

82 

11 

761 

71 

35 

30 

8.  509  6080 

8.512  3204 

0.  87808 

2.  1275 

5.  7137 

31 

77 

3197 

854 

79 

39 

32 

75 

9D 

900 

83 

41 

33 

73 

83 

947 

87 

43 

34 

70 

76 

0.  87993 

90 

45 

35 

68 

69 

0.88039 

94 

47 

36 

66 

62 

085 

2.  1298 

49 

37 

63 

55 

131 

2.  1302 

51 

38 

61 

48 

177 

06 

52 

39 

59 

41 

223 

10 

54 

40 

8.509  6056 

8.512  3133 

0.  88269 

2.1314 

5.  7156 

7.712 

41 

54 

26 

315 

17 

58 

42 

52 

19 

360 

21 

60 

43 

49 

12 

406 

25 

62 

44 

47 

3105 

452 

29 

64 

45 

45 

3028 

498 

33 

66 

46 

42 

91 

543 

37 

68 

47 

40 

•   84 

589 

40 

70 

48 

37 

77 

63J 

44 

72 

49 

35 

70 

680 

"  48 

74 

50 

8.  509  6033 

8.512  3063 

0.  88726 

2.1352 

5.  7176 

51 

30 

56 

771 

56 

78 

5> 

28 

48 

816 

59 

80 

53 

26 

41 

862 

63 

82 

54 

23 

34 

907 

67 

84 

55 

21 

27 

952 

71 

86 

56 

18 

20 

'  0.88998 

74 

88 

57 

16 

13 

0.  89043 

78 

90 

58 

14 

3006 

088 

82 

92 

59 

11 

2998 

133 

86 

94 

60 

8.  509  6009 

8.  512  2991 

0.  89178 

2.  1390 

5.7196 

7.719 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE   17°. 


218 


Lat. 

log  A 
diff.l"=-0.04 

logB 
diff.l"=-0.12 

logC 
diff.l"=-0.73 

logD 
diff.l"=+0.06 

logE 
diff.l"=+0.03 

logF 

o    / 

17  00 

8.509  6009 

8.512  2991 

0.89178 

2.1390 

5.  7196 

77719 

1 

06 

84 

223 

93 

97 

2 

04 

77 

268 

2.  1397 

99 

3 

6002 

70 

313 

2.  1401 

5.7201 

4 

5999 

62 

358 

04 

03 

05 

97 

55 

403 

08 

05 

6 

94 

48 

448 

12 

07 

7 

92 

41 

493 

16 

09 

8 

90 

34 

538 

19 

11 

9 

87 

26 

583 

23 

13 

10 

8.509  5985 

8.  512  2919 

0.89627 

2.  1427 

5.  7215 

11 

82 

12 

672 

30 

17 

12 

,   80 

2905 

717 

34 

19 

13 

78 

2897 

761 

38 

21 

14 

75 

90 

806 

42 

23 

15 

73 

83 

850 

45 

25 

16 

70 

76 

895 

49 

27 

17 

68 

68 

939 

53 

29 

18 

65 

61 

0.89984 

56 

81 

19 

63 

54 

0.90028 

60 

33 

20 

8.  509  5961 

8.512  2846 

0.90072 

2.1464 

5.  7235 

7.726 

21 

58 

39 

117 

67 

37 

22 

56 

32 

161 

71 

39 

23 

53 

24 

205 

75 

41 

24 

.51 

17 

249 

78 

43 

25 

48 

10 

294 

82 

45 

26 

46 

2802 

338 

85 

47 

27 

44 

2795 

382 

89 

49 

28 

41 

88 

426 

93 

51 

29 

39 

80 

470 

2.  14% 

53 

30 

8.  509  5936 

8.512  2773 

0.  90514 

2.1500 

5.  7255 

31 

34 

66 

558 

04 

57 

32 

31 

58 

602 

07 

59 

33 

29 

51 

646 

11 

61 

34 

26 

44 

689 

14 

64 

35 

24 

36 

733 

18 

66 

36 

21 

29 

777 

22 

68 

37 

19 

21 

821 

25 

70 

38 

16 

14 

864 

29 

72 

39 

14 

2707 

908 

32 

74 

40 

8.  509  5912 

8.  512  2699 

0.90952 

2.  1536 

5.  7276 

7.732 

41 

09 

92 

0.90995 

39 

78 

42 

07 

84 

0.  91039 

43 

80 

43 

04 

77 

082 

47 

82 

44 

5902 

69 

126 

50 

84 

45 

5899 

62 

169 

54 

86 

46 

97 

55 

212 

57 

88 

47 

94 

47 

256 

61 

90 

48 

92 

40 

299 

64 

92 

49 

89 

32 

342 

68 

94 

50 

8.509  5887 

8.512  2625 

0.91386 

2.  1571 

5.7296 

51 

84 

17 

429 

75 

5.  7298 

52 

82 

10 

472 

78 

5.7300 

53 

79 

2602 

515 

82 

02 

54 

77 

2595 

558 

85 

04 

55 

74 

87 

601 

89 

06 

56 

72 

80 

644 

92 

08 

57 

69 

72 

687 

96 

11 

58 

67 

65 

730 

2.  1599 

13 

59 

64 

57 

773 

2.  1603 

15' 

60 

8.509  6862 

8.512  2550 

0.  91816 

2.1606 

5.  7317 

7.738 

214 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

sLATITUDE  18°. 


Lat. 

log  A 
diff.  1"=  -0.04 

logB 
diff.l"=-0.13 

logC 
diff.l"=+0.70 

logD 
diff.  1"=+0.06 

logE 
diff.  1"=+0.03 

logF 
diff.  10'=  +3.0 

o  •  i 
18  00 

8.  509'  5862 

8.  512  2550 

0.  91816 

2.1606 

5.  7317 

7.738 

1 

59 

42 

859 

10 

19 

2 

57 

35 

902 

13 

21 

3 

54 

27 

945 

17 

23 

4 

52 

19 

0.  91987 

20 

25 

05 

49 

12 

0.  92030 

24 

27 

6 

46 

8.  512  2504 

073 

27 

29 

7 

44 

8.  512  2497 

115 

*  31 

31 

8 

41 

89 

158 

34 

33 

9 

39 

81 

201 

38 

35 

10 

8.509  5836 

8.512  2474 

0.  92243 

2.  1641 

5.  7337 

11 

34 

66 

286 

44 

39 

12 

31 

59 

328 

48 

41 

13 

29 

51 

371 

51 

44  ' 

14 

26 

43 

413  ' 

55 

46 

15 

24 

36 

456 

58 

48 

16 

21 

28 

498 

62 

50 

17 

19 

20 

540 

65 

52 

18 

16 

13 

582 

68 

54 

19 

13 

8.  512  2405 

625 

72 

56 

20     8.509  5811 

8.  512  2397 

0.  92667 

2.  1675 

5.  7358 

7.744 

21          08 

90 

709 

79 

60 

22          06 

82 

751 

82 

62 

23          03 

74 

793 

85 

64 

24     8.  509  5801 

67 

836 

89 

67 

25     8.  509  5798 

59 

878 

92 

69 

26          96 

51 

920 

95 

71 

27  i         93 

44 

0.  92962 

2.  1699 

73 

28 

90 

36 

0.  93004 

2.  1702 

75 

29 

88 

28 

046 

•  06 

77 

30 

8.  509  5785 

8.  512  2320 

0.  93088 

2.  1709 

5.  7379 

31 

83 

13 

129 

12 

81 

32 

80 

8.  512  2305 

171 

16 

83 

33 

78 

8.512  2297 

213 

19 

85 

34 

75 

90 

255 

22 

88 

35 

72 

82 

296 

26 

90 

36 

70 

74 

338 

29 

92 

37 

67 

66 

380 

32 

94 

38 

65 

58 

421 

36 

96 

39 

62 

51 

463 

39 

5.  7398 

40 

8.509  5759 

8.  512  2243 

0.  93505 

2.  1742 

5.7400 

7.750' 

41 

57 

35 

546 

46 

02 

42 

54 

27 

588 

49 

05 

43 

52 

19 

629 

52 

07 

44 

49 

12 

671 

56 

09 

45 

46 

8.  512  2204 

712 

59 

11 

46 

44 

8.  512  2196 

753 

62 

13 

47 

41 

88 

795 

65 

15 

48 

39 

80 

836 

69 

17 

49 

36 

72 

877 

72 

19 

50  " 

8.  509  5733 

8.512  2165 

0.  93919 

2.  1775 

5.7422 

51 

31 

57 

0.  93960 

79 

24 

52 

28 

49 

0.94001 

82 

26 

53 

25 

41 

042 

85 

28 

54 

23 

33 

083 

88 

30 

55 

20 

25 

125 

92 

32 

56 

18 

17 

166 

95 

34 

57 

15 

10 

207 

2.  1798 

37 

58 

12 

8.  512  2102 

248 

2.  1801 

39 

59 

10 

8.  512  2094 

289 

05 

41 

60 

8.  509  5707 

8.  512  2086 

.  0.94330 

2.  1808 

5.7443 

7.756 

GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE.  19°. 


215 


Lat. 

log  A 
diff.  1"=-  0.04 

logB        logC        logD 
diff.l"=-0.13  diff.l"  =  +0.67  diff.  1"==  +0.05 

logE 
diff.  1"  =  +0.04 

logF 
diff.  10'  =  +2.7 

o   / 

19  00 

8.509  5707 

8.  512  2086 

0.  94330 

2.1808 

5.  7443 

7.756 

1 

04 

78 

370 

11 

.  45 

2 

8.509  5702 

70 

411 

14 

47 

3 

8.509  5699 

62 

452 

18 

49 

4 

96 

54 

493 

21 

52 

05 

94 

46 

534 

24 

54 

6 

91 

38 

575 

27 

56 

7' 

89 

30 

615 

30 

58 

8 

86 

22 

656 

34 

60 

9 

83 

14 

697 

37 

62 

10 

8.509  5681 

8.5122006 

0.  94737 

2.1840 

5.7464 

11 

78 

8.512  1999 

778 

43 

67 

12 

75 

91 

819 

46 

69 

13 

73 

83 

859 

50 

71 

14 

70 

75 

900 

53 

73 

15          67 

67 

940 

56 

75 

16          65 

59 

0.  94981 

59 

78 

17          62 

51 

0.95021 

62 

80 

18          59 

43 

061 

66 

82 

19  !        57 

35 

102 

69 

84 

20     8.  509  5654 

8.  512  1927 

0.95142 

2.  1872 

5.7486 

7.761 

21 

52 

19 

182 

75 

88 

22 

49 

11 

223 

78 

91 

23 

46 

8.512  1903 

263 

81 

93 

24 

43 

8.  512  1895 

303 

34 

95 

25 

41 

87 

344 

88 

97 

26 

38 

79 

384 

91 

5.  7499 

27 

35 

71 

424 

94 

5.7501 

28 

33 

63 

464 

2.  1897 

04 

29  i         30 

55 

504 

2.1900 

06 

30    8.  509  5627 

8.512  1847 

0.95544 

2.1903 

5.7508 

31 

25 

38 

584 

07 

10 

32 

22 

30 

624 

10 

12 

33 

19 

22 

664 

13 

15 

34 

16 

14 

704 

16 

17 

35 

14 

8.  512  1806 

744 

19 

19 

36 

11 

8.512  1798 

784 

22 

21 

37 

08 

90 

824 

25 

23 

38 

06 

82 

863 

28 

26 

39 

03 

74 

903 

31 

28 

40 

8.509  5600 

8.  512  1766 

0.  95943 

2.  1934 

5.7530 

7.767 

41 

8.  509  5598 

57 

0.  95983 

38 

32 

42 

95 

49 

0.96022 

41 

34 

43 

92 

41 

062 

44 

37 

44 

89 

33 

102 

47 

39 

45 

87 

25 

142 

50 

41 

46 

84 

17 

•  181 

53 

43 

47 

81 

08 

221 

46 

48 

78 

8.512  1700 

260 

59 

48 

49 

76 

8.512  1692 

300 

62 

50 

50 

8.509  5573 

8.512  1684 

0.96339 

2.1965 

5.  7552 

51 

70 

75 

379 

68 

54 

52 

68 

67 

418 

71 

57 

53 

65 

59 

457 

74 

59 

54 

62. 

51 

497 

77 

61 

55 

59 

43 

536 

80 

63 

56 

67 

34 

575 

83 

65 

57 

54 

26 

615 

M 

68 

58 

51 

18 

654 

89 

70 

59 

48 

10 

693 

92 

72 

60 

y.509  5546 

8.512  1602 

0.  96733 

2.1996 

5.  7574 

7.  772 

216 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  20°. 


Lat. 

log  A 
diff.l"=  -0.05 

logB 
diff.l"=-0.14 

logC 
diff.l"=+0.64 

logD 
diff.l"  =  +0.05 

logE 
diff.l"=+0.04 

logF 
diff.lO'=+2.5 

O     1 

20  00 

8.  509  5546 

8.512  1602 

0.  96733 

2.1996 

5.  7574 

7.772 

1 

43  . 

8.  512  1593 

772 

2.1999 

77  - 

2 

40 

85 

811 

2.2002 

79 

3 

37 

77 

850 

05 

81 

4 

35 

68 

889 

08 

83 

05 

32 

60 

928 

11 

86 

6 

29 

52 

0.  96967 

14 

88 

.   7 

26 

44 

0.97006 

17 

90 

' 

8 

24 

35 

045 

20 

92 

9 

21 

27 

084 

23 

94 

10 

8.  509  5518 

8.512  1519 

0.  97123 

2.  2026 

5.  7597 

11 

15 

10' 

162 

28 

5.  7599 

12 

12 

8.512  1502 

201 

31 

5.  7601 

13 

10 

8.  512  1494 

240 

34 

03 

14 

07 

&5 

279 

37 

06 

15 

04 

77 

318 

40 

08 

16 

8.  509  5501 

69 

356 

43 

10 

17 

8.509  5499 

60 

395 

46 

12 

18 

96 

5? 

434 

49 

15 

19 

93 

44 

472 

52 

17 

20  i   8.  509  5490 

8.512  1435 

0.  97511 

2.2055 

5.  7619 

7.777 

21          87 

27 

550 

58 

21 

22          85 

18 

588 

61 

24 

23 

82 

10 

627 

64 

26 

24 

79 

8.512  1402 

666 

67 

28 

25 

76 

8.  512  1393 

704 

70 

30 

26 

73 

85 

743 

73 

33 

27 

71 

76 

781 

76 

35 

28 

68 

68 

819 

79 

37 

29 

65 

60 

858 

81 

40 

30 

8.5095462 

8.512  1351 

0.  97896 

2.  2084 

5.  7642 

31 

59 

43 

935 

87 

44 

32 

57 

34 

0.  97973 

90 

46 

33 

54 

26 

0.  98011 

93 

49 

34 

51 

17 

050 

96 

51 

35 

48 

09 

088 

2.2099 

53 

36 

45 

8.512  1301 

126 

2.  2102 

55 

37 

42 

8.512  1292 

164 

05 

58 

88 

40 

84 

203 

08 

60 

39 

37 

75 

241 

10 

62 

40 

8.  509  5434 

8.512  1267 

0.  98279 

2.2113 

5.  7664 

7.782 

41 

31 

58 

317 

16 

67 

42 

28 

50 

355 

19 

69 

43 

25 

41 

393 

22 

71 

4-4 

23 

33 

431 

25 

74 

45 

20 

24 

469 

28 

76 

46 

17 

16 

507   • 

31 

78 

47 

14 

8.512  1207 

545 

33 

81 

48 

11 

8.512  1199 

583 

36 

83 

49 

08 

90 

621 

39 

85 

50 

8.509  5406 

8.512  1182 

0.  98659 

2.  2142 

5.7688 

51 

03 

73 

697 

45 

90 

52 

8.  509  5400 

64 

735 

48 

92 

53 

8.  509  5397 

56 

773 

50 

91 

54 

94 

47 

811 

53 

97 

55 

91 

39  * 

848 

56 

5.  7699 

56 

88 

30 

886 

59 

5.  7701 

57 

86 

21 

924 

62 

04 

58 

83 

13 

962 

65 

06 

59 

80 

8.512  1104 

0.  98999 

67 

08 

60 

8.509  6377 

8.512  1096 

0.  99037 

2.  2170 

5.7711 

7.787 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  21°. 


217 


log  A 
***•   diff.  1"=  -0.05 

logB 
diff.  1"=  -0.15 

logC 
diff.l"=  +0.062  diff 

logD 
.1"=+0.04 

logE 
diff.  1"=  +0.04 

logF 
diff.  10'  =+2.2 

o   / 
21  00 

8.  509  5377 

8.512  1096 

0.99037 

2.  2170 

5.  7711 

7.787 

1 

74 

87 

075 

73 

13 

2 

71 

79 

112 

76 

15 

3 

68 

70 

150 

79 

18 

4 

66 

62 

187 

81 

20 

05 

63 

53 

225 

84 

22 

6 

60 

45 

262 

87 

24 

7 

57 

36 

300 

90 

27 

8 

54 

27 

337 

93 

29 

9 

51 

19 

375 

95 

31 

10 

8.509  5348 

8.512  1010 

0.99412 

2.  2198 

5.  7734 

11 

46 

8.512  1002 

450 

2.  2201 

36 

12 

43 

8.512  0993 

487 

04 

38 

13 

40 

84 

524 

07 

41 

14 

37 

76 

562 

09 

43 

15 

34 

67 

599 

12 

45 

16 

31 

58 

636 

15 

48 

17 

28 

'  50 

673 

18 

50 

•  18 

25 

41 

711 

20 

52 

19          22 

32 

748 

23 

55 

20    8.  509  5320 

8.512  0924 

0.99785 

2.2226 

5.7757 

7.791 

21 

17 

15 

822 

29 

59   - 

22 

14 

8.  512  0906 

859 

31 

62 

23 

11 

8.  512  0897 

8% 

34 

64 

24 

08 

89  ' 

933 

37 

66 

25 

05 

80 

0.99971 

40 

69 

. 

26 

8.509  5302 

71 

1.00008 

42 

71 

27 

8.  509  5299 

62 

045 

45 

73 

28 

96 

54 

082 

48 

76 

29 

93 

45 

119 

50 

78 

30 

8.509  5290 

8.512  0836 

1.00156 

2.2253 

5.7780 

31 

88 

27 

192 

56 

83 

32 

85 

19 

229 

59 

85 

33 

82 

10 

266 

61 

87 

34 

79 

8.  512  0801 

303 

64 

90 

35 

76 

8.5120792 

340 

67 

92 

36 

73 

84 

377 

69 

94 

37 

70 

75 

413 

72 

97 

38 

67 

66 

450 

75 

5.  7799 

39 

64 

57 

487 

78 

5.7802 

40 

8.5095261 

8.5120748 

1.00524 

2.2280 

5.7804 

7.  796 

41 

58 

39 

560 

83 

06 

42 

55 

31 

597 

86 

09 

43 

52 

22 

634 

88 

11 

44 

49 

13 

670 

91 

13 

45 

46 

8.5120704 

707 

94 

16 

46 

44 

8.  512  0695 

743 

96 

18 

47 

41 

86 

780 

2.  2299 

20 

48 

38 

78 

816 

2.  2301 

23 

49 

35 

69 

853 

04 

25 

50 

8.509  5232 

8.512  0660 

1.00890 

2.2307 

5.  7828 

51 

29 

51 

926 

09 

30 

52 

26 

42 

962 

12 

32 

53 

23 

33 

1.00999 

15 

35 

54 

20 

24 

1.01035 

17 

37 

55 

17 

15 

072 

20 

40 

56 

14 

8.512  0606 

108 

23 

42 

57 

11 

8.  512  0598 

144 

25 

44 

.  58 

08 

89 

181 

28 

47 

59 

05 

80 

217 

31 

49 

60 

8.509  5202 

8.  512  0571 

1.  01253 

2.2333 

5.7851 

7.800 

218 


GEOGRAPHIC    TABLES    AND    FOEMTJLAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  22°. 


Lat. 

log  A 
diff.l"=-0.05 

logB 
diff.l"=-0.15 

logC 
diff.l"=+0.59 

logD 
diff.l"=+0.04 

logE 
diff.l"=+0.04 

logF 
diff.lO'=+2.0 

0     / 

22  00 

8.  509  5202 

8.  512  0571 

1.  01253 

2.  2333 

5.  7851 

7.800 

1 

8.  509  5199 

62 

289 

36 

54 

2 

96 

53 

326 

38 

56 

3 

93 

44 

362 

41 

59 

4 

90 

35 

398 

44 

61 

05 

87 

26 

434 

46 

63 

6 

84 

17 

470 

49 

66 

7 

81 

8.  512  0508 

506 

51 

68 

8 

78 

8.  512  0499 

542 

54 

71 

9 

75 

90 

578 

57 

73 

10. 

8.  509  5172 

8.  512  0481 

1.  01615 

2.2359 

5.  7875 

11 

69 

72 

651 

62 

78 

12 

66 

63 

687 

64 

80 

13 

63 

54 

723 

67 

83 

14 

60 

45 

759 

70 

85 

15 

57 

36 

794 

72' 

87 

16 

54 

27 

830 

75  . 

90 

17 

51 

18 

866 

77 

92 

18 

48 

09 

902 

80 

95 

19 

45 

8.512  0400 

938 

83 

97 

20 

8.  509  5142 

8.  512  0391 

1.  01974 

2.  2385 

5.  7899 

7.804 

21 

39 

82 

1.02010 

88 

5.  7902 

22 

36 

73 

045 

90 

04 

23 

33 

64 

081 

.  93 

07 

24: 

30 

55 

117 

95 

09 

25 

27 

46 

153 

2.  2398 

11 

26 

24 

37 

188 

2.2400 

14 

27 

21 

..  28 

224 

03 

16 

28 

18 

19 

260 

06 

19 

29 

15 

10 

295 

08 

21 

30 

8.  509  5112 

8.  512  0301 

1.  02331 

2.2411 

5.7924 

31 

09 

8.  512  0292 

367 

13 

26 

32 

06 

83 

402 

16 

28 

33 

03 

73 

438 

18 

31 

34 

8.  509  5100 

64 

473 

2] 

33 

35 

8.  509  5097 

55 

509 

23 

36 

36 

94 

46 

544 

26 

38 

37 

91 

37 

580 

28 

41 

38 

88 

28 

615 

31 

43 

39 

85 

19 

651 

33 

45 

40  j   8.  509  5082 

8.  512  0210 

1.02686 

2.2436 

5.  7948 

7.808 

41          79 

8.  512  0200 

721 

38 

50 

42 

76 

8.512  0191 

757 

41 

53 

43          72 

82 

792 

43 

55 

44 

69 

73 

828 

46 

58 

45 

66 

64 

863 

48 

60 

46 

63 

55 

898 

51 

62 

47 

60 

46 

933 

53 

65 

48 

57 

36  . 

1  -02969 

56 

67 

49 

54 

27 

1  -03004 

58 

70 

50 

8.509  5051' 

8.  512  0118 

1.  03039 

2.  2461 

5.  7972 

51 

48 

09 

074 

63 

75 

52 

45 

8.  512  0100 

109 

66 

77 

53 

.  42 

8.  512  0090 

145 

68 

80 

54 

39 

81 

180 

70 

82 

55 

36 

72 

215 

73 

84 

56 

33 

63 

250 

75 

87 

57 

30 

54 

285 

78 

89 

58 

27 

44 

320 

80 

92 

59 

23 

35 

365 

83 

94 

60 

8.509  5020 

8.  512  0026 

1.03390 

2.  2485 

5.7997 

7.812 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


219 


TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  23°. 


Lat. 

log  A 
diff.  1"=—  0.05 

logB 
diff.  1"=  -0.16 

logC 
diff.  1"=  +0.57 

logD 
diff.  1"=+  0.04 

logE 
diff.  1"=  +0.04 

logF 
diff.  10'  =  +1.8 

i  o   r 
23  00     8.  509  5020 

8.  512  0026 

1.03390 

2.  2485 

5.  7997 

7.  812 

1 

17 

17 

425 

88 

5.  7999 

2 

14 

8.5120008 

460 

90 

5.  8002 

3 

11 

8.511  9998 

495 

93 

04 

4 

08 

89 

530 

95 

07 

05          05 

80 

565 

2.  2497 

09 

6    8.509  5002 

71 

600 

2.2500 

12 

7     8.  509  4999 

61 

634 

02 

14 

% 

52 

669 

05 

16 

93 

43 

704 

07 

19 

10     8.  509  4990 

8.511  9934 

1.  03739 

2.  2510 

5.  8021 

11          87 

24 

774 

12 

24 

12          83 

15 

809 

14 

26 

13          80 

8.  511  9906 

843 

17 

29 

* 

14          77 

8.511  9896 

878 

19 

31 

lo          74 

87 

913 

22 

34 

16          71 

78 

947 

24 

36 

17          68 

68 

1.03982 

26 

39 

18          65 

59 

1.04017 

29 

41 

19          62 

50 

052 

31 

44 

20     8.  509  4959 

8.  511  9840 

1.04086 

2.2534 

5.8046 

7.816 

21          55 

31 

121 

36 

49 

22          52 

22 

155 

38 

51 

23          49 

12 

190 

41 

54 

24          46 

8.511  9803 

224 

43 

56 

25          43 

8.511  9794 

259 

45 

59 

26          40 

84 

293 

48 

61 

27          37 

75 

328 

50 

64 

28          34 

66 

362 

53 

66 

29          31 

56 

397 

55 

69 

30    8.  509  4927 

8.511  9747 

1.04431 

2.2557 

5.8071 

31          24 

37 

466 

60 

74 

32          21 

28 

500 

62 

76 

33          18 

19 

534 

64 

79 

34 

15 

09 

569 

67 

81 

35 

12 

8.511  9700 

603 

69 

84 

36 

09 

8.511  9690 

637 

71 

86 

37  :         05 

81 

672 

74 

89 

38     8.  509  4902 

71 

706 

76 

91 

39     8.  509  4899 

62 

740 

78 

93 

40     8.  509  4896 

8,511  9653 

1.04775 

2.2581 

5.8096 

7.  819 

41  !         93 

43 

809 

83 

5.  8099 

42          90 

34 

843 

85 

5.  8101 

43 

87 

24 

877 

88 

04 

44 

83 

15 

911 

90 

06 

45 

80 

8.511  9605 

945 

92 

09 

46 

77 

8.511  9596 

1.04980 

95 

11 

47 

74 

86 

1.05014 

97 

14 

48 

71 

77 

048 

2.  2599 

16 

49  . 

68 

67 

082 

2.  2601 

19 

50 

8.509  4865 

8.511  9558 

1.  05116 

2.2604 

5.  8121 

51 

61 

48 

150 

06 

24 

52 

58 

39 

184 

09 

26 

53 

55 

29 

218 

11 

29 

54 

52 

20 

252 

13 

31 

55 

49 

10 

286 

16 

34 

56 

45 

8.511  9501 

320 

18 

36 

57 

42 

8.511  9491 

354  , 

20 

39 

58 

'39 

82 

388 

23 

41 

59 

36 

72 

422 

25 

44 

60 

8.509  4833 

8.511  9463 

1.05456 

2.  2627 

5.8146 

7.823 

220 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  24°. 


Lat. 

log  A 
cliff.  1"=  -0.06 

logB 
cliff.  1"=  -0.16 

logC 
cliff.  1"=  +0.56 

logD 
diff.l"=+0.04 

log  E        log  F 
cliff.  1"==  +0.04  cliff.  10'=  +1.6 

o   r 

24  00 

8.  509  4833 

8.511  9463 

1.05456 

2.  2627 

5.  8146        7.  823 

1 

30 

53 

490 

29 

49 

2 

26 

44 

523 

31 

51 

3 

23 

34 

557 

34 

54 

4 

20 

24 

591 

36 

57 

05 

17 

15 

625 

08 

59 

6 

14 

8.511  9405 

658 

41 

62 

7 

10 

s.511  9396 

692 

43 

C4 

8 

07 

86 

726 

45 

67 

9 

04 

77 

760 

47 

69 

10  |   8.509  4801 

8.511  9367 

1.05794 

2.2650 

5.  8172 

11 

8.  509  4798 

58 

827 

52 

74 

13 

94 

48 

861   • 

54 

77 

13 

91 

-  38 

894 

56 

79 

14 

88 

29 

928 

59 

82 

15 

85 

19 

.  962 

61 

86 

16 

82 

09 

1.05995 

63 

87 

17 

78 

8.511  9300 

1.06029 

65 

90 

18 

75 

8.511  9290 

062 

•   68 

92 

19          72 

81 

096 

70 

95 

20     8.  .509  4769 

s.  oil  9271 

1.06130 

2.  2672 

5.8197        7.826 

21          66 

61 

163 

74 

5.8200 

22 

62 

52 

197 

77 

02 

28 

/  59 

42 

230 

79 

05 

24 

56 

32 

263 

81 

07 

25 

53 

23 

297 

83 

10 

26 

50 

13 

330 

85 

13 

•  >- 

46 

8.511  9203 

364 

88 

15 

28 

43 

8.511  9194 

397 

90 

18 

29 

40 

84 

431 

92 

20 

30 

8.509  4737 

S.all  9174 

1.06464 

2.  2694 

5.8223 

31 

33 

65 

497 

96 

25 

32 

30 

55 

530 

2.  2699 

28 

33 

27 

45 

.564 

2.  2701 

31 

34 

24 

35 

597 

03 

33 

35 

20 

26 

630 

05 

36 

36 

17 

16 

664 

07 

38 

37 

14 

8.511  9106 

697 

10 

41 

38 

11 

8.511  9096 

730 

12 

43 

on 

07 

87 

763 

14 

46 

40 

8.  509  4704 

8.511  9077 

1.06797 

2.2716 

5.  8249        7.  829 

41 

8.  509  4701 

67 

830 

•18 

51 

42 

8.  509  4698 

58 

863 

20 

54 

43 

94 

48 

896 

23 

56 

44 

91 

38 

929 

25 

59 

45 

S8 

28 

962 

27 

61 

46 

85 

18 

1.  06995 

29 

64 

47 

81 

8.511  9009 

1.  07028 

31 

67 

48 

78 

8.  511  8999 

061 

33 

69 

49 

75 

89 

095 

36 

•  72 

60 

8.509  4672 

8.511  8979 

1.07128 

2.  2738 

5.  8274 

51 

68 

70 

161 

40 

77 

52 

65 

60 

194 

42 

80 

53 

62 

50 

226 

44 

82 

54 

59 

40 

259 

46 

85 

55 

.55 

30 

292 

49 

87 

56 

52 

21 

325 

51 

90 

57 

49 

11 

358 

53 

92 

58 

45 

8.511  8901 

391 

55 

95 

59 

42 

8.  511  8891 

424 

57 

5.  8298 

60 

8.  509  4639 

8.  511  8881 

1.07457 

2.2759 

5.8300        7.832 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computation* — Continued. 

LATITUDE  25°. 


221 


T  at           1°&  A 

Lat-    diff.l"=-0'06 

logB 
diff.l"=-0-16 

logC 
diff.l"=-r0'54  d 

logD 

iff.  1"=  +0-0 

logE 
3  difM"=+0-04 

logF 
diff.!0'  =  +l-5 

o   / 

25  00    8.  509  4639 

8.511  8881 

1.  07457 

2.  2759 

5.8300 

7.832 

1          36 

71 

490 

61 

03 

2 

32 

62 

523 

63 

05 

3 

29 

52 

555 

66 

08 

4 

26 

42 

588 

68 

11 

05 

23 

32 

621 

70 

13 

6 

19 

22 

654 

72 

16 

7 

16 

12 

687 

74 

18 

8 

13 

8.511  8802 

719 

76 

21 

9 

09 

8.511  8793 

752 

78 

24 

10    8.5094606 

8.511  8783 

1.07785 

2.  2780 

5.  8326 

11          03 

73 

817 

82 

29 

12     8.  509  4600 

63 

850 

85 

32 

13    8.  509  45% 

53 

883 

87 

34 

14          93 

43 

915 

89 

37 

15 

90 

33 

948 

91 

39 

16 

86 

23 

1.07981 

93 

42 

17 

83 

13 

1.0S013 

95 

45 

18 

80 

8.511  8704 

046 

97 

47 

19 

76 

8.511  8694 

078 

2.  2799 

50 

20  !   8.  509  4573 

8.511  8684 

1.08111 

2.2801 

5.  8352 

7.835 

21          70 

74 

143 

03 

55 

22          66 

64 

176 

05 

59 

23 

63 

51 

208 

07 

60 

24 

60 

44 

241 

10 

63 

25 

56 

34 

273 

12 

66 

26 

53 

24 

306 

14 

68 

27 

50 

14 

338 

16 

71 

28 

8.511  8604 

370 

18 

73 

29          43 

8.511  8594 

403 

20 

76 

30     8.  509  4540 

8.511  8584 

1.08435 

2.  2822 

5.  8379 

31  '         37 

74 

468 

24 

81 

32  !        33 

64 

500 

26 

84 

33 

30 

54 

532 

28 

87 

34 

26 

44 

565 

30 

89 

35 

23 

34 

597 

32 

.  92 

36 

20 

24 

629 

34 

94 

37 

17 

14 

662 

36 

5.  8397 

38 

13 

8.511  8504 

694 

38 

5.8400 

39 

10 

8.  511  8494 

726 

40 

02 

40    8.  509  4507 

8.511  8484 

1.08758 

2.2842 

5.8405 

7.838 

41          03 

74 

791 

44 

08 

42     8.  509  4500 

64 

823 

46 

10 

43     8.509  44% 

54 

855 

48 

13 

44          93 

44 

887 

50 

16 

45 

90 

34 

919 

52 

18 

46 

86 

24 

951 

54 

21 

47 

83 

14 

1.08984 

56 

24 

48 

80 

8.511  8404 

1.09016 

58 

26 

49 

76 

8.  511  8393 

048 

60 

29 

50 

8.  509  4473 

8.511  8383 

1.09080 

2.  2862 

5.  8431 

51 

70 

73 

112 

64 

34 

52 

66 

63 

141 

66 

37 

53 

63 

53 

176 

68 

39 

54 

60 

43 

208 

70 

42 

55 

56 

33 

240 

72 

45 

56 

53 

23 

272 

74 

47 

57 

50 

13 

304 

76 

50 

58 

46 

8.511  8303 

336 

78 

53 

59 

43 

8.  511  8293 

-368 

80 

55 

60 

8.509  4439 

8.511  8283 

1.09400 

2.2882 

.  5.8458 

7.841 

222 


GEOGRAPHIC    TABLES    ADD    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  26°. 


Lat. 

log  A 
diff.l"=-0-06 

logB 
diff.l"=-0-17  c 

logC 

Liff.l"=+0 

logD 
52  diff.l"=-fO-03 

log  E       log  F 
diff.l"=+0-04  diff.lO'  =  +l-3 

o   / 

» 

26  00 

8.  509  4439 

8.511  8283 

1.09400 

2.2882 

5.8458 

7.841 

1 

36 

72 

432 

84 

61 

2 

33 

62 

464 

86 

63 

3 

29 

52 

496 

88 

66 

4 

26 

42 

527 

90 

69 

05 

22 

32 

'  559 

92 

71 

6 

19 

22 

591 

94 

74 

7 

16 

12 

623 

96 

77 

8 

12 

8.  511  8201 

655 

2.  2898 

79 

9 

09 

8.511  8191 

687 

2.2900 

82 

10 

8.509  4406 

8.511  8181 

1.  09718 

2.  2902 

5.8485 

11 

8.  509  4402 

71 

750 

04 

88 

12 

8.  509  4399 

61 

782 

06 

90 

13 

95 

51 

814 

08 

93 

14 

92 

40 

845 

10 

96 

15 

88 

30 

877 

12 

5.  8498 

16 

85 

20 

909 

14 

5.8501 

17 

82 

10 

940 

16 

04 

18 

78 

8.  511  8100 

1.09972 

18 

06 

19 

75 

8.511  8089 

1.10004 

20 

09 

20 

8.  509  4372 

8.  511  8079 

1.  10036 

2.2922 

5.8512 

7.844 

21 

68 

69 

067 

23 

14 

22 

65 

59 

099 

25 

17 

23 

61 

48 

130 

27 

20 

24 

58 

38 

162 

29 

22 

25 

54 

28 

194 

31 

25 

26 

51 

18 

225 

33 

28 

27 

48 

8.  511  8008 

257 

35 

30 

28 

44 

8.  511  7997 

288 

37 

33 

29 

41 

87 

320 

39 

36 

30 

8.  509  4337 

8.511  7977 

1.10351 

2.2941 

5.8539  . 

31 

34 

67 

383 

43 

41 

32 

31 

56 

414 

45 

44 

33 

27 

46 

446 

47 

47 

34 

24 

36 

477 

48 

49 

35 

20 

25 

509 

50 

52 

36 

17 

15 

540 

52 

55 

37 

13 

8.511  7905 

571 

54 

57 

38 

10 

8.511  7895 

603 

56 

60 

39 

07 

84 

634 

58 

63 

40 

8.  509  4303 

8.511  7874 

1.10666 

2.2960 

5.8566 

7.846 

41 

8.  509  4300 

.64 

697 

62 

68 

42  ' 

8.  509  4296 

53 

728 

63 

71 

43 

93 

43 

760 

65 

74 

44 

89 

33 

791 

67 

76 

45 

86 

22 

822 

69 

79 

46 

83 

12 

854 

71 

82 

47 

79 

8.511  7802 

885 

73 

85 

48 

76 

8.511  7791 

916 

75 

87 

49 

72 

81 

947 

77 

90  •, 

50 

8.  509  4269 

8.511  7771 

1.  10979 

2.2978 

5.8593 

51 

65 

60 

1.  11010 

80 

95 

52 

62 

50 

041 

82 

5.8598 

53 

58 

40 

072 

84 

5.  8601 

54 

55 

29 

103 

86 

04 

55 

52 

19 

134 

88- 

06 

56 

48 

8.511  7709 

166 

89 

09 

57 

45 

8.511  7698 

197 

91 

12 

58 

41 

88 

228 

93 

14 

* 

59 

38 

77 

259 

95 

17 

60 

8.509  4234 

8.511  7667 

1.11290 

2.  2997 

5.  8620 

7.849 

GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  27°. 


223 


Tit        log  A 
Lat-    diff.l"=-0.06 

logB 
diff.l"=-0.18 

logC 
diff.l"=+0.51 

logD' 
diff.l"=+0.03 

logE 
diff.l"=+0.05 

logF 
diff.lO'  =  +l.l 

o   / 
27  00 

8.509  4234 

8.511  7667 

1.11290 

A  2997 

5.8620 

7.849 

1 

31 

57 

321 

2.2999 

23 

2 

27 

46 

352 

2.  3001 

25 

3 

24 

36 

383 

03 

28 

4 

J  20 

25 

414 

04 

31 

06 

17 

15 

445 

06 

34 

6 

13 

8.511  7605 

476 

08 

36 

7 

10 

8.511  7594 

507 

10 

39 

8 

06 

84 

538 

12 

42 

9 

03 

73 

569 

14 

44 

10    8.  509  4200 

8.511  7563 

1.11600 

2.3015 

5.  8647 

11     8.5094196 

53 

631 

17 

50 

12 

93 

42 

662 

19 

53 

13 

89 

32 

693 

21 

56 

14 

86 

21 

724 

23 

58 

15 

82 

11 

755 

24 

61 

16 

79 

8.511  7500 

786 

26 

64 

17 

75 

8.511  7490 

817 

28 

66 

18 

72 

79 

848 

30 

69 

19 

68 

69 

878 

32 

72 

20 

8.  509  4165 

5.511  7458 

1.  11909 

2.3033 

5.8675 

7.851 

21 

61 

48 

940 

35 

77 

22 

58 

37 

1.  11971 

37 

80 

23 

54 

27 

1.12002 

39 

83 

24 

51 

16 

032 

41 

86 

25 

47 

8.511  7406 

063 

42 

88 

26 

44 

8.511  7395 

094 

44 

91 

27 

40 

85 

126 

46 

94 

28 

37 

74 

156 

48 

97 

29 

33 

64 

186 

50 

5.8699 

30 
31 

8.  509  4130 

8.511  7353 
43 

1.12217 
248 

2.  3051 
53 

5.  8702 
05 

32 

23 

32 

278 

55 

08 

33 

19 

22 

309 

57 

10 

34 

16 

11 

340 

58 

13 

35' 

12 

8.511  7301 

370 

60 

16 

36 

08 

8.511  7290 

401 

62 

19 

37 

05 

80 

432 

64 

22 

38 

8.509  4101 

69 

462 

65 

24 

39 

8.  509  4098 

58 

493 

67 

27 

40 

8.509  4094 

8.511  7248 

1.12623 

2.3069 

5.8730 

7.853 

41 

91 

37 

554 

70 

33 

42 

87 

27 

584 

72 

35 

43 

84 

16 

615 

74 

38 

44 

80 

8.511  7206 

646 

76 

41 

45 

77 

8.511  7195 

676 

78 

44 

46 

73 

84 

707 

79 

46 

47 

70 

74 

737 

81 

49 

48 

66 

63 

768 

83 

52 

49 

63 

53 

798 

85 

55 

50 

8.  509  4059 

8.511  7142 

1.12829 

2.3086 

5.  8757 

51 

56 

31 

859 

88 

60 

52 

52 

21 

889 

90 

63 

53 

49 

10 

920 

91 

66 

54 

45 

8.  511  7100  • 

950 

93 

69 

55 

41 

8.511  7089 

1.12981 

95 

72 

56 

38 

78 

1.  13011 

97 

74 

57 

34 

68 

041 

2.3099 

77 

58 

31 

57 

072 

2.3100 

80 

59 

27 

46 

102 

02 

83 

60 

8.509  4024 

8.611  7036 

1.13132 

2.  3104 

5.8785 

7.855 

224 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  28°. 


Lat. 

log  A 
diff.l"=-0.06 

logB 
3iff.l"=-0.1£ 

logC 
diff.l"=+0.50 

logD 
diff.l"=+0.03 

logE 
diff.l"=+0.05 

logF 
diff.lO"=+1.0 

o    / 
28  00 

8.509  4024 

8.511  703(> 

1.  13132 

2.3104 

5.8785 

7.855 

1 

20 

25 

163 

05 

88 

2 

17 

14 

193 

07 

91 

3 

13 

8.511  7004 

223 

09 

94 

4 

10 

8.  511  6993 

254 

10 

97 

05 

06 

82 

284 

12 

5.8799 

6 

8.  509  4002 

72 

314 

14 

5.8802 

7 

8.  509  3999 

61 

345 

16 

05 

8 

95 

50 

375 

17 

08 

9          92 

40 

405 

19 

11 

10 

8.  509  3988 

8.511  6929 

1.13435 

2.  3121 

5.8813 

11 

85 

18 

465 

22 

16 

12 

81 

8.511  6908 

496 

24 

19 

13 

78 

8.  511  6897 

526 

26 

22 

14 

•  74 

86 

556 

27 

25 

15 

70 

75 

586 

29 

27 

16 

67 

65 

616 

31 

30 

17 

63 

54 

646 

32 

33 

18 

60 

43 

677 

34 

36 

19 

56 

33 

707 

36 

39 

20 

8.  509  3952 

8.511  6822 

1.  13737 

2.3137 

5.8841 

7.857 

21 

49 

11 

767 

39 

44 

22 

45 

8.  511  6800 

797 

41 

47 

23 

42 

8.511  6790 

827 

42 

50 

24 

38 

79 

857 

44 

53 

25 

35 

68 

887 

46 

55 

26 

31 

57 

917 

47 

58 

27 

27 

47 

947 

49 

61 

28 

24 

36 

1.13977 

51 

64 

29 

20 

25 

1.  14007 

52 

67 

30 

8.  509  3917 

8.  511  6714 

1.14037 

2.3154 

5.  8870 

31 

13 

8.511  6704 

067 

56 

72 

32 

09 

8.511  6693 

097 

57 

75 

•33 

06 

82 

127 

59 

78 

34 

8.  509  3902 

71 

157 

61 

81 

35 

8.  509  3899 

61 

187 

62 

84 

36 

95 

50 

217 

64 

87 

37 

92 

39 

247 

65 

89 

38 

88 

28 

277 

67 

92 

39 

84 

17 

307 

69 

95 

40 

8.  509  3881 

8.511  6607 

1.  14337 

2.  3170 

5.8898 

7.859 

41 

77 

8.  511  6596 

366 

72 

5.8901 

42 

73 

85 

396 

74 

04 

43 

70 

74 

426 

75 

06 

44 

66 

63 

456 

77 

09 

45 

63 

52 

486 

78 

12 

46 

59 

42 

516 

80 

15 

47 

55 

31 

545 

82 

18 

48 

52 

20 

575 

83 

21 

49 

48 

8.511  6509 

605 

85 

23 

50 

8.  509  3845 

8.511  6498 

1.14635 

2.3187 

5.8926 

51 

41 

87 

664 

88 

29 

52 

37 

76 

694 

90 

32 

53 

34 

66 

724 

91 

35 

54 

30 

55 

754 

93 

38 

55 

26 

44 

783 

95 

40 

56 

23 

33 

813 

96 

43 

57 

19 

22 

843 

98 

46 

58 

16 

11 

872 

2.3199 

49 

59 

12 

8.511  6400 

902 

2.  3201 

52 

60 

8.509  3808 

8.511  6389 

1.14932 

2.3203 

5.8956 

7.861 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  29°. 


225 


Lat. 

leg  A 
diff.l"=-0.06 

logB 
diff.l"=-0.18 

logC 
diff.l"=+0.49 

logD 
diff.l"=+0.03 

log  E        log  F 
diff.l"=+0.05  diff.lO'=+O.S 

o   / 
29  00 

8.509  3808 

8.511  6389 

1.  14932 

2.  3203 

5.  8955         7.  861 

1 

05 

78 

961 

04 

58 

2 

8.509  3801 

68 

1.  14991 

06 

60 

3 

8.  509  3797 

57 

1.15021 

07 

63 

4 

94 

46 

050 

09 

66 

05 

90 

35 

080 

10 

69 

6 

86 

24 

109 

12 

72 

7 

83 

13 

139 

14 

75 

8 

79 

8.511  6302 

168 

15 

78 

9 

76 

8.511  6291 

198 

17 

80 

10 

8.  509  3772 

8.511  6280 

1.15228 

2.  3218 

5.  8983 

11 

68 

69 

257 

20 

86 

12 

65 

58 

287 

21 

89 

13 

61 

47 

316 

23 

92 

14 

57 

36 

346 

25 

95 

15 

54 

26 

375 

26 

5.8998 

16 

50 

15 

405 

28 

5.9000 

17 

46 

8.511  6204 

434 

29 

03 

18 

43 

8.511  6193 

464 

31 

06 

19          39 

82 

493 

32 

09 

•  20    8.509  3735 

8.511  6171 

1.15522 

2.  3234 

5.  9012         7.  863 

21          32 

60 

552 

35 

15 

22 

28 

49 

581 

37 

18 

23 

24 

38 

611 

38 

21 

24 

21 

27 

640 

40 

23 

25 

17 

16 

670 

42 

26 

26 

13 

8.511  6105 

699 

43 

29 

27 

10 

8.511  6094 

728 

45 

32 

28 

06 

83 

758 

46 

35 

29 

8.  509  3702 

72 

787 

48 

38 

30 

8.  509  3699 

8.511  6061 

1.  15816 

2.3249 

5.9041 

31 

95 

50 

846 

51 

43 

32 

91 

39 

875 

52 

46 

33 

88 

28 

904 

54 

49 

34 

84 

17 

934 

55 

52 

35 

80 

K.511  6006 

963 

57 

55 

36 

77 

8.511  5995 

1.15992 

58 

58 

37 

73 

84 

1.16021 

60 

61 

38 

69 

73 

051 

61 

64 

39 

66 

61 

080 

63 

67 

40 

8.  509  3662 

S.511  5950 

1.16109 

2.  3264 

5.  9069         7.  8C.4 

41 

58 

39 

138 

66 

72 

42 

55 

28 

167 

67 

75 

43 

51 

17 

197 

69 

78 

44 

47 

8.511  5906 

226 

70 

81 

45 

44 

8.511  5895 

255 

7'2 

84 

46 

40 

84 

284 

73 

87 

47 

36 

73 

313 

75 

90 

48 

33 

62 

343 

76 

93 

49 

29 

51 

372 

78 

% 

50 

8.  509  3625 

S.511  5840 

1.16401 

2.  3279 

5.  9098 

51 

21 

29 

430 

81 

5.  9101 

52 

18 

18 

459 

82 

04 

53 

14 

8.511  5806 

488 

84 

07 

54 

19 

8.511  5795 

517 

85 

10 

55 

07 

84 

546 

87 

13 

56 

8.  509  3603 

73 

575 

88 

16 

57 

8.  509  3599 

62 

604 

90 

19 

58 

% 

51 

633 

91 

22 

59 

92 

40 

663 

93 

25 

60 

8.5093588 

8.511  5729 

1.16692 

2.  3294 

5.  9127         7.  866 

1 

46061—08 15 


226 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 


LATITUDE  30°. 


Lat. 

log  A 
diff.  1"=  -0.06 

log 
diff.  1"= 

B 

=  -0.19 

logC 
diff.  1"=  +0.48 

logD 
diff.  1"=  +0.02 

logE 
diff.  1"=  +0.05 

logF 
diff.  10'=  +0.7 

o   / 
30  00 

8.509  3588 

8.  511 

5729 

1.16692 

2.  3294 

5.  9127 

7.866 

1 

84 

18 

721 

96 

30 

2 

81 

8.511 

5706 

750 

97 

33 

3 

77 

8.511 

5695 

778 

2.  3298 

36 

4 

73 

84 

807 

2.3300 

39 

05 

69 

73 

836 

01 

42 

6 

66 

62 

865 

03 

45 

7 

62 

51 

894 

04 

48 

8 

58 

40 

923 

06 

51 

9 

55 

28 

952 

07 

54 

10' 

8.  509  3551 

8.511 

5617 

1.  16981 

2.3309 

5.  9157 

11 

47 

8.511 

5606 

1.  17010 

10 

59 

12 

43 

8.511 

5595 

'   039 

12 

62 

13 

40 

84 

068 

13 

65 

14 

36 

73 

097 

14 

68 

15 

32 

61 

126 

16 

71 

10 

29 

50 

155 

17 

74 

17 

25 

39 

184 

18 

77 

18 

21 

28 

212 

20 

80 

19          17 

17 

241 

22 

83 

20 

8.  509  3514 

8.511 

5505 

1.17270 

2.  3323 

5.  9186 

•  7.867. 

21 

10 

8.511 

5494 

299 

24 

89 

22 

06 

83 

328 

26 

92 

23 

8.  509  3502 

72 

357 

27 

95 

24 

8.509  3499 

61 

385 

29 

5.  9198 

25 

95 

49 

414 

30 

5.9200 

26 

91 

38 

443 

32 

03 

27 

88 

27 

472 

33 

06 

28 

84 

16 

500 

34 

09 

29 

80 

8.511 

5404 

529 

36 

12 

30 

8.  509  3476 

8.511 

5393 

1.17558 

2.3337 

5.  9215 

31 

72 

82 

587 

39 

18 

32 

69 

71 

615 

40 

21 

33 

65 

59 

644 

41 

24 

34 

61 

48 

673 

43 

27 

35 

57 

37 

701 

44 

30 

36 

54 

26 

730 

46 

33 

37 

50 

14 

759 

47 

36 

38 

46 

8.511 

5303 

788 

48 

39 

39 

42 

8.511 

5292 

816 

50 

42 

40 

8.  509  3439 

8.511 

5281 

1.17845 

2.3351 

5.  9245 

7.869 

41 

35 

69 

874 

53 

48 

42 

31 

58 

902 

54 

Kl 

43 

27 

47 

931 

55 

53 

44 

24 

35 

959 

57 

56 

45 

20 

24 

1.  17988 

58 

59 

46 

16 

13 

1.18017 

59 

62 

47 

12 

8.511 

5202 

045 

61 

65 

48 

09 

8.511 

5190 

074 

62 

68 

49 

05 

79 

102 

64 

71 

50 

8.  509  3401 

8.511 

5168 

1.18131 

2.3365 

5.  9274 

51 

8.  509  3397 

56 

160 

66 

77 

52 

94 

45 

188 

68 

80 

53 

90 

34 

217 

69 

83 

54 

86 

22 

245 

70 

86 

55 

82 

11 

274 

72 

89 

56 

78 

8.511 

5100 

302 

73 

92 

57 

75 

8.511 

5088 

331 

74 

95 

.58 

71 

77 

359 

76 

5.  9298 

59 

67 

66 

388 

77 

5.  9301 

60 

8.509  3363 

s.  f>i  1 

5054 

1.18416 

2.3379 

5.  9304 

7.870 

GEOGKAPHIC    TABLES    AND    FOKMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  31°. 


227 


L«t. 

log  A 
diff.l"=-0.06 

logB 
diff.l"=-0.19 

logC 
diff.l"=+0.47 

logD 
diff.l"=+0.02 

logE 
diff.l"=+0.05 

logF 
diff.  10'=  +0.5 

O     1 

31  00 

8.509  3363 

8.  511  CJ54 

1.18416 

•2.  3379 

ft.  9304 

7.870 

1 

60 

43 

445 

80 

07 

2 

56 

32 

473 

81 

10 

3 

52 

20 

501 

83 

13 

4 

48 

8.511  5009 

530 

84 

16 

05 

44 

8.511  4998 

558 

85 

19 

6 

41 

86 

587 

87 

22 

7 

37 

75 

615 

88 

25 

8 

33 

64 

643 

89 

28 

9 

29 

52 

672 

91 

31 

10 

S.  509  3325 

S.511  4941 

1.18700 

•2.  3392 

ft.  9334 

11 

22 

29 

729 

93 

37 

12 

18 

18 

757 

95 

39 

13 

14 

8.511  4907 

785 

96 

42 

14 

10 

8.  511  4895 

813 

97 

45 

15 

06 

84 

842 

2.  3399 

48 

•16 

8.509  3303 

72 

870 

2.3400 

51 

17 

8.5093299 

61 

898 

01 

54 

18 

95 

50 

927 

03 

57 

19 

91 

38 

955 

04 

60 

20    8.  509  3287 

8.511  4827 

1.18983 

•2.  3405 

5.9363 

7.871 

21          84 

15 

1.  19012 

06 

66 

22          80 

8.511  4804 

040 

08 

69 

23 

76 

8.  511  4793 

068 

09 

72 

24 

72 

81 

096 

10 

75 

25 

68 

70 

125 

12 

78 

26 

65 

58 

153 

13 

81 

27 

61 

47 

181 

14 

84 

28 

57 

35 

209 

16 

87 

29 

53 

24 

238 

17 

90 

30 

8.  509  3249 

8.511  4713 

1.19266 

2.  3418 

5.  9393 

31 

46 

8.511  4701 

294 

20 

96 

32 

42 

8.  511  4690 

322 

21 

5.  9399 

33 

38 

78 

351 

22 

5.9402 

34 

34 

67 

379 

23 

05 

35 

30 

55 

407 

25 

08 

36 

26 

44 

435 

26 

11 

37 

23 

32 

463 

27 

14 

38 

19  . 

21 

491 

29 

17 

39 

15 

8.511  4609 

520 

30 

20 

40 

8.  509  3211 

8.511  4598 

1  .  19548 

2.3431 

ft.  9423 

7.  872 

41 

07 

86 

576 

32 

26 

42 

03 

75 

604 

34 

29 

43 

8.509  3200 

63 

632 

35 

32 

44 

8.  509  3196 

52 

660 

36. 

35 

45 

92 

40 

688 

37 

38 

46 

88 

29 

716 

39 

41 

47 

84 

17- 

744 

40 

44 

48 

81 

8.511  4506 

772 

41 

47 

49 

77 

8.511  4494 

800 

43 

50 

50 

8.  509  3173 

8.511  4483 

1.19828 

2.3444 

5.9453 

51 

69 

71 

856 

45 

56 

52 

65 

60 

884 

46 

59 

H 

61 

48 

912 

48 

62 

54 

57 

37 

940 

49 

65 

55 

54 

25 

968 

50 

68 

56 

50 

14 

1.19996 

51 

72 

57 

46 

8.511  4402 

1.20024 

53 

75 

58 

42 

8.511  4391 

052 

54 

78 

59 

38 

79 

080 

55 

81 

60 

8.  509  3134 

8.511  4368 

1.  20108 

2.3456 

ft.  9484 

7.873 

228 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  32°. 


Lat. 

log  A 
diff.  1"=  -0.06 

log 
diff.  l"= 

B 

=  —0.19 

log  C 
diff.  1"=  +0.46 

logD 
diff.  1"=  +0.02 

log  E        log  F 
diff.  1"-=  +0.05  diff.  10'  =  +0.3 

o   / 
32  00 

8.509  3134 

8.  511 

4368 

1.20108 

2.  3456 

5.  9484        7.  873 

1 

31 

56 

136 

57 

87 

2 

27 

44 

164 

59 

90 

3 

23 

33 

192 

60 

93 

4 

19 

21 

220 

61 

96 

05 

15 

8.511 

4310 

248 

62 

5.  9499 

6 

11 

8.511 

4298 

276 

64 

5.9502 

7 

07 

87 

304 

65 

05 

8 

04 

75 

332 

66 

08 

9 

8.509  3100 

63 

360 

67 

11 

10 

8.  509  3096 

S.  51  1 

4252 

1.20387 

2.  3469 

5.  9514 

11 

92 

40 

415 

70 

17 

12 

88 

29 

443 

71 

20 

13 

84 

17 

471 

72 

23 

14 

80 

8.511 

4205 

499 

73 

26 

15 

76 

8.511 

4194 

527 

75 

29 

16 

73 

82 

555 

76 

32 

17 

69 

71 

582 

77 

35 

18 

65 

59 

610 

78 

38 

19 

61 

47 

638 

79 

41 

20     <s.  509  3057 

8.511 

4136 

1.20666 

2.  3481 

5.9544        7.874 

21          53 

24 

694 

82 

47 

22 

49 

13 

722 

83 

50 

23 

46 

8.511 

4101 

749 

84 

53 

24 

42 

8.511 

4089 

777 

85 

56 

25 

38 

78 

805 

87 

60 

26 

34 

66 

833 

88 

63 

27 

30 

54 

860 

89 

66 

28 

26 

43 

888 

90 

69 

29 

22 

31 

916 

91 

72 

30 

8.  509  3018 

8.511 

4020 

1.  20944 

2.  3493 

5.9575 

31 

15 

8.511 

4008 

971 

94 

78 

32 

11 

8.511 

3996 

1.20999 

95' 

81 

33 

07 

85 

1.21027 

96 

84 

34 

8.  5C9  3003 

73 

054 

97 

87 

35 

8.509  2999 

61 

082 

2.3499 

90 

36 

95 

50 

110 

2.3500 

93 

37 

91 

38 

137 

01 

% 

38 

87 

26 

165 

02 

5.  9599 

39 

83 

15 

193 

03 

5.  9602 

40 

8.  509  2980 

8.511 

3903 

1.21220 

2.3504 

5.  %05        7.  875 

41 

76 

8.511 

3891 

248 

06 

08 

42 

72 

79 

276 

07 

11 

43 

68 

68 

303 

08 

15 

44 

64 

.  56 

331 

09 

18 

45 

60 

44 

358 

10 

21 

46 

56 

33 

386 

11 

24 

47 

52 

21 

414 

13 

27 

48 

48 

8.511 

3809 

441 

14 

30 

19 

44 

8.511 

3798 

469 

15 

33 

50 

8.  509  2940 

8.511 

3786 

1.214% 

2.  3516 

5.  9636 

51 

37 

-74 

524 

17 

39 

52 

33 

63 

551 

18 

42 

53 

29 

51 

579 

19 

45 

54 

25 

39 

607 

21 

48 

55 

21 

27 

634 

22 

51 

56 

17 

16 

662 

23 

54 

57 

13 

8.511 

3704 

689 

24 

58 

58 

09 

8.511 

3692 

717 

25 

61 

59 

05 

80 

744 

26 

64 

60 

8.  509  2901 

8.511 

3669 

1.21772 

2.  3527 

5.9667        7.875 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computation* — Continued. 
LATITUDE  33°. 


229 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.20 

logC 
diff.l"=+0.45 

logD 
diff.l"=+0.02 

logE 

diff.i"=+o.o:> 

logF 
diff.lO'=+0.2 

o   / 

33  00 

8.509  2901 

8.511  3669 

1.  21772 

2.  3527 

5.  9667 

7.875 

1 

8.  509  2897 

57 

799 

29 

70 

2 

94 

45 

827 

30 

73 

3 

90 

33 

854 

31 

76 

4 

86 

22 

882 

32 

79 

05 

82 

8.511  3610 

909 

33 

82 

6 

78 

8.511  3598 

937 

34 

85 

1 

74 

86 

964 

35 

88 

8 

70 

75 

1.21992 

36 

92 

9 

66 

63 

1.22019 

38 

95 

10 

8.509  2862 

8.511  3551 

1.22047 

2.  :«39 

5.  9698 

11 

58 

39 

074 

40 

5.  9701 

12 

54 

28 

101 

41 

04 

13 

51 

16 

129 

42 

07 

14 

47 

8.511  3504 

156 

43 

10 

15 

43 

8.511  3492 

184 

44 

13 

16 

39 

80 

211 

45 

16 

17 

35 

69 

238 

46 

19 

18 

31 

57 

266 

48 

22 

19 

27 

45 

293 

49 

26 

20 

8.509  2823 

8.511  3433 

1.22321 

2.3550 

r>.  9729 

7.  876 

21 

19 

21 

348 

51 

32 

22 

15 

8.511  3410 

375 

52 

35 

23 

11 

8.511  3398 

403 

53 

38 

24 

07 

86 

430 

54 

41 

25 

8.  509  2803 

74 

457 

55 

44 

26 

8.  509  2799 

62 

485 

56 

47 

27 

95 

51 

512 

57 

50 

28 

91 

39 

539 

58 

53 

29 

88 

27 

567 

60 

57 

30 

s.  T>09  2784 

8.  511  3315 

1.22594 

•2.  3561 

5.  9760 

31 

80 

8.511  3303 

621 

62 

63 

32 

76 

8.511  3291 

648 

63 

66 

33 

72 

80 

676 

64 

69 

34 

68 

68 

703 

fc  65 

72 

35 

64 

56 

730 

66 

75 

36 

60 

44 

757 

67 

78 

37 

56 

32 

785 

68 

81 

38 

52 

20 

812 

69 

85 

39 

48 

8.511  3209 

839 

70 

88 

40 

8.509  2744 

8.511  3197 

1.22866 

2.3571 

5.  9791 

7.876 

41 

40 

85 

893 

72 

94 

42 

36 

73 

921 

73 

5.  9797 

43 

32 

61 

948 

75 

5.  9800 

44 

28 

49 

1  -22975 

76 

03 

77 

06 

45 

24 

37 

1.23002 

46 

20 

25 

029 

78 

10 

47 

16 

13 

057 

79 

13 

48 

12 

8.511  3102 

084 

80 

16 

49 

08 

8.511  3090 

111 

81 

19 

50 

8.  509  2704 

8.511  3078 

1.23138 

2.  3582 

5.  9822 

51 

8.  509  2701 

66 

165 

83 

25 

52 

8.  509  2697 

54 

192 

H4 

28 

53 

93 

42 

220 

85 

31 

54 

89 

30 

247 

86 

35 

55 

85 

18 

274 

87 

38 

56 

81 

8.511  3006 

301 

88 

41 

57 

77 

8.511  2995 

328 

89 

44 

58 

73 

83 

355 

90 

47 

59 

69 

71 

382 

91 

50 

CO 

8.509  2665 

8.511  2959 

1.23409 

2.  3592 

5.  9853 

7.877 

230 


GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 


LATITUDE  34°. 


Lat. 

log  A 

logB 
'  diff.  1"=-0.20 

logC 
diff.  1"=  +0.45 

logD 
diff.  l"=  +0.02 

logE 
diff.  1"=  +0.05 

logF 
diff.  10'=  +0.0 

o   / 

34  00 

8.  509  2665 

8.511  2959 

1.23409 

2.  3592 

5.  9853 

7.877 

1 

61 

47 

437 

93 

'  57 

2 

57 

35 

464 

94 

60 

3 

53 

23 

491 

95 

63 

4 

49 

8.511  2911 

518 

96 

66 

05 

45 

8.511  2899 

545 

97 

69 

6 

41 

87 

572 

98 

72 

7 

37 

75 

599 

2.3599 

75 

8 

33 

63 

626 

2.3600 

79 

9          29 

51 

653 

01 

82 

10     8.  509  2625 

8.511  '.840 

1.23680 

2.  3602 

5.  9885 

11          21 

28 

707 

03 

88 

12          17 

16 

734 

04 

91 

13          13 

8.511  804 

761 

05 

94 

14          09 

8.511  1792 

788 

06 

5.  9897 

15          05 

80 

815 

07 

5.9901 

16     8.  509  2601 

68 

842 

08 

04 

17     8.  509  2597 

56 

869 

09 

07 

18          93 

44 

896 

10 

10 

19          89 

32 

923 

11 

13 

20 

8.  509  2585 

8.511  1720 

1.  23950 

•2.  3612 

5.  9916 

7.877 

21 

81 

8.511  2708 

1.23977 

13 

19 

22 

77 

8.  511  -2C96 

1.24004 

14 

23 

23 

73 

84 

031 

15 

26 

24 

6J 

72 

058 

16 

29 

25 

65 

60 

085 

17 

32 

26 

61 

48 

112 

18 

35 

27 

57 

36 

139 

19 

38 

28 

53 

24 

165 

20 

42 

29 

49 

12 

192 

21 

45 

30 

8.  .509  2545 

8.511  2600 

1.2  219 

•1.  3.  22 

5.  9948 

31 

41 

8.511  2588 

246 

23 

51 

32 

37 

76 

27.S 

24 

54 

33 

33 

64 

3JO 

25 

57 

34 

29 

52 

327 

26 

61 

35 

25 

40 

354 

27 

64 

36 

21 

28 

381 

28 

67 

37 

17 

16 

408 

29 

70 

38 

13 

8.  511  2504 

431 

30 

73 

39 

09 

8.  511  2492 

461 

31 

76 

40 

8.  509  2505 

8.511  2480 

1.24488 

2.  3632 

r>.  9980 

7.  877 

41 

8.  509  2501 

68 

515 

33 

83 

42 

8.  509  2497 

56 

542 

34 

86 

43 

93 

44 

569 

35 

89 

44 

89 

32 

595 

.  36 

92 

45 

85 

20 

622 

37 

96 

46 

81 

8.511  2408 

649 

38 

5.9999 

47 

77 

8.  511  2396 

676 

39 

6.0002 

.  48 

73 

84 

703 

40 

05 

49 

69 

72 

729 

08 

41 

50 

8.  509  2465 

8.611  2360 

1.24756 

2.3642 

6.0011 

51 

61 

48 

783 

43 

15 

52 

57 

35 

810 

43 

18 

53 

53 

23 

837 

44 

21 

54 

49 

8.511  2311 

863 

45 

24 

-55 

45 

8.611  2299 

890 

46 

27 

56 

41 

87 

917 

47 

31 

57 

37 

V5 

944 

48 

34 

68 

33 

63 

970 

49 

37 

59 

29 

51 

1.24997 

50 

40 

60 

8.509  2425 

8.511  2239 

1.26024 

2.3651 

6.0043 

7.877 

GEOGRAPHIC  TABLES  AND  FOEMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  35°. 


231 


Lat. 

log  A 
d  iff.  1"=  -0.07 

log 
diff.  1"= 

B 

=  -0.20 

logC 
diff.  1"=  +0.44 

logD 
diff.  1"=  +0.01 

logE 
diff.l"=+0.05 

logF 
diff.  10'=  +0.0 

o   / 
35  00 

8.  509  2425 

8.511 

2239 

1.25024 

•2.  3651 

6.0043 

7.877 

1 

21 

27 

050 

52 

47 

2 

17 

15 

077 

53 

50 

3 

13 

8.511 

2203 

101 

54 

53 

4 

09 

8.511 

2191 

131 

55 

56 

06 

05 

78 

157 

56 

59 

6 

8.  509  2401 

66 

184 

56 

63 

7 

8.  509  23% 

54 

211 

57 

66 

8 

92 

42 

237 

58 

69 

9 

88 

30 

264 

59 

72 

10 

8.509  2384 

8.511 

2118 

1.25291 

2.3660 

6.  0075 

11 

80 

8.511 

2106 

317 

61 

79 

12 

76 

8.511 

2094 

344 

62 

82 

13 

72 

82 

371 

63 

85 

14 

68 

70 

397 

64 

88 

15 

64 

57 

424 

65 

91 

16 

60 

45 

451 

66 

95 

17 

56 

33 

477 

66 

6.0098 

18 

52 

21 

504 

67 

6.  0101 

19 

48 

8.511 

2009 

531 

68 

04 

20 

8.509  2344 

8.511 

1997 

1.25557 

2.3669 

6.  0107 

7.877 

21 

40 

85 

584 

70 

11 

22 

36 

72 

610 

71 

14 

23 

32 

60 

637 

72 

17 

24 

28 

48 

664 

73 

20 

25 

24 

36 

690 

74 

23 

26 

20 

24 

717 

75 

27 

27 

16 

12 

743 

75 

30 

28 

12 

8.511 

1900 

770 

76 

33 

29 

08 

8.511 

1887 

796 

71 

36 

30 

8.509  2304 

8.511 

1875 

1.25823 

•2.  3678 

(1.  0140 

31 

8.509  2300 

6:5 

850 

79 

43 

32 

8.  509  2296 

51 

876 

80 

46 

33 

92 

39 

903 

81 

49 

34 

87 

27 

929 

82 

52 

35 

98 

15 

956 

82 

56 

36 

79 

8.511 

1802 

1.25982 

83 

59 

37 

75 

8.511 

1790 

1.26009 

84 

62 

38 

71 

78 

035 

85 

65 

39 

67 

K 

062 

86 

69 

40 

8.509  2263 

8.  51  1 

1754 

1  .  26088 

2.  3B87 

6.0172 

7.877 

41 

59 

41 

115 

88 

75 

42 

55 

29 

141 

MS 

78 

43 

51 

17 

168 

W 

81 

44 

47 

8.  511 

170f> 

194 

90 

85 

45 

43 

8.511 

1693 

221 

91 

88 

46 

39 

80 

247 

9-2 

91 

47 

35 

68 

274 

93 

94 

48 

31 

56 

300 

94 

6.  0198 

49 

27 

44 

327 

94 

6.  0201 

50 

8.  509  2222 

8.511 

1632 

1.26353 

•2.  3159ft 

6.  0204 

51 

18 

20 

380 

96 

07 

52 

14 

8.511 

1607 

406 

97 

11 

53 

10 

8.511 

159o 

432 

98 

14 

54 

06 

83 

459 

99 

17 

55 

8.  509  220-2 

71 

485 

2.  3699 

20 

56 

fc.  509  '2198 

58 

512 

•2  3700 

24 

57 

91 

46 

538 

01 

27 

58 

90 

34 

565 

0-2 

30 

59 

86 

22 

591 

03 

33 

60 

8.  509  2182 

8.511 

1510 

1.26617 

•2.3701 

0.  0237 

7.877 

232 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  36°. 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.  1"=  -0.20 

logC 
diff.  1"=  +0.44 

logD 
diff.  1"=  +0.01 

log  E        log  F 
diff.l"=+0.05  diff.lO'=-0.2 

o   / 

36  00 

8.  509  2182 

8.511  1510 

1.26617 

2.3704 

6.  0237        7.  877 

1 

78 

8.511  1497 

644 

04 

40 

2 

74 

85 

670 

05 

43 

3 

70 

73 

697 

06 

46 

4 

65 

61 

723 

07 

50 

05 

61 

48 

749 

08 

53 

6 

57 

36 

776 

09 

56 

7 

53 

24 

802 

09 

59 

8 

49 

8.511  1412 

828 

10 

63 

9 

45 

8.511  1399 

855 

11 

66 

10 

8.  509  2141 

8.511  1387 

1  .  26881 

2.  3712 

6.  0269 

11 

37 

75 

908 

13 

12 

33 

63 

934 

13 

76 

13 

29 

50 

960 

14 

79 

14 

25 

38 

1.  26987 

15 

82 

15 

21 

26 

1.27013 

16 

85 

16 

16 

14 

039 

17 

89 

17 

12 

8.  511  1301 

066 

17 

92 

18 

08 

8.511  1289 

092 

18 

95 

19 

04 

77 

118 

19 

6.0299 

20 

8.  509  2100 

8.511  1265 

1.27145 

2.  3720 

6.  0302        7.  877 

21 

8.  509  2096 

52 

171 

21 

05 

22 

92 

40 

197 

21 

08 

23 

88 

28 

223 

22 

12 

24 

84 

15 

250 

23 

15 

25 

80 

8.511  1203 

276 

24 

18 

26 

75 

8.511  1191 

302 

25 

21 

27 

71 

79 

329 

25 

25 

28 

67 

66 

355 

26 

28 

29 

63 

54 

381 

27 

31 

30 

8.  509  2059 

8.511  1142 

1.27407 

2.  3728 

6.  0334 

31 

55 

29 

434 

29 

38 

32 

51 

17 

460 

29 

41 

33 

47 

8.511  1105 

486 

30 

44 

34 

43 

8.511  1092 

512 

31 

48 

35 

39 

80 

539 

32 

51 

36 

35 

68 

565 

32 

54 

37 

30 

56 

591 

33 

57 

38 

26 

43 

617 

34 

61 

39 

22 

31 

644 

35 

64 

40 

8.  509  2018 

8.511  1019 

1.27670 

2.  3735 

6.  0367        7.  877 

41 

14 

8.511  1006 

696 

36 

71 

42 

10 

8.511  0994 

722 

37 

74 

43 

06 

82 

748 

38 

77 

44 

8.509  2002 

69 

775 

39 

80 

45 

8.509  1998 

57 

SOI 

39 

84 

46 

93 

45 

827 

40 

87 

47 

89 

32 

853 

41 

90 

48 

85 

20 

879 

42 

94 

49 

81 

N.511  0908 

905 

42 

6.  0397 

50 

8.509  1977 

-s.511  0895 

1  .  27932 

2.3743 

6.  0400 

51 

73 

83 

958 

44 

03 

52 

69 

71 

1.27984 

45 

07 

53 

65 

58 

1.2X010 

45 

10 

54 

61 

46 

036 

46 

13 

55 

56 

34 

062 

•47 

17 

56 

52 

21 

088 

48 

20 

57 

48 

S.511  0809 

114 

48 

23 

58 

-II 

<s  511  0797 

141 

49 

27 

59 

-10 

167 

50 

30 

60 

8.509  1936 

8.511  U772 

1  2819:5 

2.  3750 

6.  0433        7.  876 

GEOGRAPHIC   TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  compulations — Continued. 
LATITUDE  37°. 


238 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.21 

logC 
diff.l"=+0.43 

logD 
diff.l"=+0.01 

log  E        log.  F 
diff.l"=+0.0;;  diff.lO'  =  -0.3 

o   / 

37  00 

8.509  1936 

8.511  0772 

1.28193 

2.  3750 

6.  0433       7.  876 

1 

32 

60 

219 

51 

37 

2 

28 

47 

245 

52 

40 

3 

23 

35 

271 

53 

43 

4 

19 

22 

297 

58 

46 

a5 

15 

8.511  0710 

324 

54 

50 

6 

11 

8.511  0698 

350 

55 

53 

7 

07 

85 

376 

56 

56 

8 

S5.09  1903 

73 

402 

50 

60 

9 

85.  09  1899 

61 

428 

57 

63 

10 

8.  509  1895 

8.511  Oti48 

1.28454 

2.  3758 

6.0466 

11 

90 

30 

480 

59 

70 

12 

8G 

23 

506 

59 

73 

13 

82 

8.511  0611 

532 

60 

76 

14 

78 

8.511  0599 

558 

01 

80  . 

15 

74 

86 

584 

61 

83 

16 

70 

74 

610 

62 

86 

17 

66 

61 

636 

03 

89  ' 

18 

62 

49 

662 

73 

93 

19 

57 

37 

688 

64  . 

96 

20 

8.509  1853 

8.511  0524  . 

1.28715 

2.  3765 

0.  0499       7.  876 

21 

49 

12 

741 

66 

6.  0503 

22 

45 

8.511  0500 

767 

66 

06 

23 

41 

8.511  0487 

793 

67 

09 

24 

37 

75 

819 

68 

13 

25 

33 

62 

845 

68 

16 

26 

28 

50 

871 

69 

19 

27 

24 

37 

897 

70 

23 

28 

20 

25 

923 

70 

26 

29 

16 

13 

949 

71 

29 

30 

8.509  1812 

8.511  0400 

1.28975 

2.  3772 

0.0533 

31 

08 

8.511  0388 

1.29001 

72 

36 

32 

04 

75 

027 

73 

39 

33 

8.509  1800 

63 

053 

74 

43 

34 

8.  509  1795 

51 

*  079 

74 

46 

35 

91 

38 

104 

75 

49 

36 

87 

26 

130 

76 

53 

37 

83 

13 

156 

76 

56 

38 

79 

8.511  0301 

182 

77 

59 

39 

75 

8.511  0288 

208 

78 

63 

40 

8.  509  1771 

S.511  0276 

1.  '2923  1 

2.  3779 

6.  0566       7.  875 

41 

66 

64 

260 

79 

69 

42 

62 

51 

286 

,80 

73 

43 

58 

39 

312 

81 

76 

44 

54 

26 

338 

81 

79 

45 

50 

14 

364 

82 

83 

46 

46 

8.511  0201 

390 

82 

86 

47 

41 

8.511  0189 

416 

83 

89 

48 

37 

76 

442 

84 

93 

49 

33 

64 

468 

84 

0.  0596 

50 

8.509  1729 

8.511  0151 

1.29494 

2.  3785 

0.0600 

51 

25 

39 

520 

86 

03 

52 

21 

26 

540 

86 

06 

53 

16 

14 

571 

87 

10 

54 

12 

8.511  010-2 

597 

88 

13 

55 

08 

8.511  008<J 

023 

88 

16 

56 

04 

77 

649 

89 

20 

57 

8.509  1700 

61 

676 

90 

23 

58 

8.509  lf.96 

52 

701 

90 

26 

59 

9-2 

39 

727 

.   91 

30 

GO 

8.509  1687 

8.511  0027 

1.29753 

2.  3792 

6.  0633        7.  874 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  38°. 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.2l 

logC 
diff.l"=+0.43 

logD 
diff.l"=+0.01 

logE 
diff.l"=+0.06 

logF 
diff.lO'=-0.4 

o   / 
38  00 

8.  509  1687 

8.511  0027 

1.29753 

2.  3792 

6.0633 

7.874 

1 

83 

14 

778 

92 

36 

2 

79 

8.  511  0002 

804 

93 

40 

3 

75 

8.  510  9989 

830 

93 

43 

.  4 

71 

77 

856 

94 

47 

05 

67 

64 

882 

95 

50 

6 

62 

52 

908 

95 

53 

7 

58 

39 

934 

96 

57 

8 

54 

27 

959 

97 

60 

9 

60 

14 

1.29985 

97 

63 

10 

8.  509  1646 

8.  510  9902 

1.30011 

2.  3798 

6.0667 

11 

42 

8.  510  9889 

037 

2.  3799 

70 

12 

37 

77 

063 

2.3800 

73 

13 

33 

64 

089 

00 

77 

14 

29 

52 

114 

01 

80 

15 

25 

39 

140 

01 

84 

16 

21 

27 

166 

02 

87 

17 

17 

14 

192 

02 

90 

18 

12 

8.  510  9802 

218 

03 

94 

19 

08 

8.  510  9789 

243 

03 

6.  0697 

20 

8.  509  1604 

8.  510  9777 

1.30269 

2.3804 

6.  0701 

7.874 

21 

8.  509  1600 

64 

295 

05 

04 

22 

8.509  1596 

52 

321 

05 

07 

23 

92 

39 

347 

06 

11 

24 

87 

27 

372 

06 

14 

25 

83 

14 

398 

07 

17 

26 

79 

8.  510  9701 

424 

08 

21 

27 

75 

8.  510  9689 

450 

08 

24 

28 

71 

77 

476 

09 

28 

29 

66 

64 

501 

09 

31 

30 

8.  509  1562 

8.510  9652 

1.30527 

2.3810 

(1.  0734 

31 

58 

39 

553 

11 

38 

32 

54 

27 

579 

11 

41 

33 

50 

14 

604 

12 

44 

34 

46 

8.510  9601 

630  ' 

12 

48 

35 

41 

8.  510  9589 

656 

13 

51 

36 

37 

76 

682 

14 

55 

37 

33 

64 

707 

14 

58 

38 

29 

51 

733 

15 

61 

39 

25 

39 

759 

15 

65 

40 

8.  509  1521 

8.  510  9526 

1.30785 

2.3816 

(>.  0768 

7.873 

41 

16 

14 

810 

16 

72 

42 

12 

8.  510  9501 

83G 

17 

75 

43 

08 

8.  510  9488 

862 

18 

78 

44 

04 

76 

887 

18 

82 

45 

8.509  1500 

63 

913 

19 

85 

46 

8.509  1495 

51 

939 

19 

89 

47 

91 

38 

965 

20 

92 

48 

87 

26 

1.30990 

20 

95 

49 

83 

13 

1.31010 

21 

G.  0799 

50 

8.  509  1479 

8.  510  9401 

1.31042 

2.  3822 

6.  0802 

51 

75 

8.  510  9388 

067 

22 

06 

52 

70 

76 

093 

23 

09 

53 

66 

63 

119 

23 

13 

54 

62 

50 

144 

24 

16 

55 

58 

38 

170 

24 

19 

56 

53 

25 

196 

25 

23 

57 

49 

13 

221 

25 

26 

58 

45 

8.510  9300 

2-17 

26 

30 

59 

41 

8.510  9287  . 

273 

27 

33 

60 

8.509  1437 

8.510  9275 

I.3TO9 

2.  3S27 

c..  os3<; 

7.872 

GEOGRAPHIC    CABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  39°. 


285 


Lat. 

log  A 
diff.  1"=  -0.07 

logB 
diff.  1"=  -0.21 

logC 
diff.  1"=  +0.43  diff 

logD 
1"=+0.01 

logE 
diff.  1"=  +0.06 

logF 
diff.lO'  =  ~0.5 

o   / 

. 

39  00 

8.509  1437 

8.510  9275 

1.31299 

2.3827 

6.0836 

7.  872 

1 

33 

62 

324 

28 

40 

2 

28 

50 

350 

28 

43 

3 

24 

37 

375 

29 

47 

4 

20 

25 

401 

29 

50 

05 

16 

8.5109212 

427 

30 

53 

6 

12 

8.  510  9199 

452 

30 

57 

7 

07 

87 

478 

31 

60 

8 

8.509  1403 

74 

504 

31 

64 

9 

8.  509  1399 

62 

529 

32 

67 

10 

8.509  1395 

8.510  9149 

1.31555 

2.  3832 

(5.0871 

11 

91 

36 

581 

33 

74 

12 

86 

24 

606 

33 

77 

13 

82 

8.510  9111 

632 

34 

81 

14 

78 

8.  510  9098 

658 

35 

84 

15 

74 

86 

683 

35 

88 

16 

70 

73 

709 

36 

91 

17 

65 

61 

734 

36 

95 

18 

61 

48 

760 

37 

6.0898 

19 

57 

36 

786 

37 

6.0902 

20 

8.509  1353 

8.  510  9023 

1.31811 

2.3838 

6.0905 

7.871 

21 

49 

8.5109010 

837 

38   ' 

08 

22 

44 

8.  510  8998 

862 

39 

12 

23 

40 

85 

888 

39 

15 

24 

36 

73 

913 

40 

19 

25 

32 

60 

939 

40 

22 

26 

28 

47 

965 

41 

26 

27 

23 

35 

1.31990 

41 

29 

28 

19 

22 

1.32016 

42 

32 

29 

15 

8.510  8909 

041 

42 

36 

30 

8.509  1311 

8.510  8897 

1.32067 

2.3843 

6.0939 

31 

07 

84 

092 

43 

43 

32 

8.509  1302 

72 

118 

44 

46 

33 

8.509  1298 

59 

144 

44 

50 

34 

94 

46 

169 

45 

53 

35 

90 

34 

195 

45 

57 

36 

86 

21 

220 

46 

60 

37 

81 

8.  510  8808 

246 

46 

63 

38 

77 

8.  510  8796 

271 

47 

67 

39 

73 

83 

297 

47 

70 

40 

8.  509  1269 

8.510  8771 

1.32323 

•2.3848 

(>.  0974 

7.870 

41 

64 

58 

348 

48 

77 

42 

60 

45 

374 

49 

81 

43 

56 

33 

399 

49 

84 

44 

52 

20 

425 

50 

88 

45 

48 

8.  510  8707 

450 

50 

91 

46 

43 

8.  510  8695 

476 

51 

95 

47 

39 

82 

501 

51 

6.0998 

48 

35 

69 

527 

52 

6.1002 

49 

31 

57 

552 

52 

05 

50 

8.  509  1227 

8.  510  8644 

1.32578 

2.3852 

6.  1008 

51 

22 

31 

603 

53 

12 

52 

18 

19 

629 

53 

15 

53 

14 

8.  510  8606 

654 

54 

19 

54 

10 

8.  5H)  8593 

680 

54 

22 

55 

06 

81 

705 

55 

26 

56 

8.509  1201 

68 

731 

55 

29 

67 

8.509  1197 

55 

756 

56 

33 

58 

93 

43 

782 

56 

36 

59 

89 

30 

807 

57 

40 

60 

8.509  1184 

8.610  8517 

1.32833 

2.3857 

6.1043 

7.869 

236 


GEOGRAPHIC    TABLES    AND    FOEMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  40°. 


Lat. 

log  A 

diff.  1"=  -0.07 

logB 
diff.l"=-0.21 

logC 
diff.  1"=+0.42 

logD 
diff.  1"=+0.01 

logE 
diff.  1"=  +0.06 

logF 
diff.  10'=—  0.7 

o   / 

40  00 

8.509  1184 

8.  510  8517 

1.32833 

2.3857 

6.  1043 

7.869 

1 

80 

8.  510  8505 

858 

58 

47 

2 

76 

8.  510  8492 

884 

58 

50 

3 

72 

79 

909 

58 

54 

4 

67 

67 

935 

59 

57 

05 

63 

54 

960 

59 

61 

6 

59 

41 

1.  32986 

60 

64 

7 

55 

29 

1.33011 

60 

67 

8 

50 

16 

037 

60 

71 

9 

46 

8.510  8403 

062 

61 

74 

10 

8.  509  1142 

8.  510  8391 

1.33088 

2.  3861 

6.1078 

11 

38 

78 

113 

62 

81 

12 

34 

65 

139 

62 

85 

13 

29 

53 

164 

63 

88 

14 

25 

40 

189 

63 

92 

15 

21 

27 

215 

64 

95 

16 

17 

15 

240 

64 

6.1099 

17 

12 

8.  510  8302 

266 

65 

6.1102 

18 

08 

8.  510  8289 

291 

65 

06 

19 

04 

77 

317 

65 

09 

20 

8.509  1100 

8.510  8264 

1.33342 

2.  3866 

(',.1113 

7.867 

21 

8.509  1096 

51 

368 

66 

16 

22 

91 

38 

393 

67 

20 

23 

87 

26 

418 

67 

23 

24 

83 

13 

444 

68 

27 

25 

79 

8.  510  8200 

469 

68 

30 

26 

74 

8.  510  8188 

495 

68 

34 

27 

70 

75 

520 

69 

37 

28 

•66 

62 

546 

69 

41 

29 

62 

50 

571 

70 

44 

30 

8.509  1057 

8.  510  8137 

1.33596 

2.  3870 

6.1148 

31 

53 

24 

622 

70 

51 

32 

49 

8.510  8111 

647 

71 

55 

33 

45 

8.  510  8099 

673 

71 

58 

34 

41 

86 

698 

72 

62 

35 

36 

73 

723 

72 

65 

36 

32 

61 

749 

72 

69 

37 

28 

48 

774 

73 

72 

38 

24 

35 

800 

73 

76 

39 

19 

23 

825 

74 

79 

40 

8.509  1015 

8.  510  8010 

1.33850 

2.  3874 

6.1183 

7.866 

41 

11 

8.  510  7997 

876 

74 

86 

42 

07 

84 

901 

75 

90 

43 

8.  509  1002 

72 

926 

75 

93 

44 

8.  509  0998 

59 

952 

76 

6.1197 

45 

94 

46 

1.33977 

76 

6.  1200 

46 

90 

33 

1.34003 

76 

04 

47 

85 

21 

028 

77 

07/ 

48 

81 

8.510  7908 

053 

77 

11 

-19 

77 

8.  510  7895 

079 

77 

15 

50 

8.  509  0973 

8.510  7883 

1.34104 

2.3878 

6.1218 

51 

68 

70 

129 

78 

22 

52 

64 

57 

155 

79 

25 

53 

60 

44 

180 

79 

29 

54 

56 

82 

206 

79 

32 

55 

52 

19 

231 

80 

36 

56 

47 

8.  510  7806 

256 

80 

39 

57 

43 

8.  510  7793 

282 

80 

43 

58 

39 

81 

307 

81 

46 

59 

34 

68 

332 

81 

50 

60 

8.509  0930 

8.510  7755 

1.34358 

2.  3882 

6.  1253 

7.864 

GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  41°. 


237 


Lat. 

log  A 
diff.l"=-0.07 

log  B        log  C 
diff.l"=-0.21  diff.l"=  +  0.4'2 

log  D        log  E        log  F 
diff.l"=+0.01  diff.l"  =  +0.06  diff.lO'  =  -0.8 

o   / 

41  00 

8.509  0930 

8.  510  7755 

1.34358 

2/3882 

6.  1253        7.  864 

1 

26 

42 

383 

82 

57 

2 

22 

30 

408 

82 

60 

3 

18 

17 

434 

83 

64 

4 

13 

8.  510  7704 

459 

83 

67 

05 

09 

8.510  7691 

484 

83 

71 

6 

05 

79 

510 

84 

75 

7 

8.509  0900 

66 

535 

84 

78 

8 

8.509  089(5 

53 

560 

84 

82 

9 

92 

40 

586 

85 

85 

10 

8.509  0888 

S.510  7628 

1.84011 

2.  3885 

6.  1289 

11 

83 

15 

636 

85 

92 

V2 

79 

8.  510  7602 

662 

86 

96 

13 

75 

8.510  7590 

687 

86 

6.  1299 

14 

71 

712 

87 

6.1303 

15 

67 

64 

738 

87 

06 

16 

62 

51 

763 

87 

10 

17 

58 

39 

788 

88 

14 

18 

54 

26 

814 

88 

17 

19 

49 

13 

839 

88 

21 

20 

8.  509  0845 

8.510  7500 

1.34864 

2.3889 

6.1324        7.863 

21 

41 

8.  510  7488 

890 

89 

28 

22 

37 

75 

915 

89 

31 

23 

32 

62 

940 

90 

35 

24 

28 

49 

965 

90 

38 

25 

24 

36 

1.34991 

30 

42 

26 

20 

24 

1.35016 

91 

46 

27 

15 

8.510  7411 

041 

91 

49 

28 

11 

8.  510  7398 

066 

91 

53 

29          07 

85 

092 

91 

56 

30     8.  509  0803 

S.  510  7373 

1.35117 

2.3892 

ti.1360 

31     8.  509  0798 

60 

142 

92 

63 

32          94 

47 

168 

92 

67 

33          90 

34 

193 

93 

70 

34          86 

22 

218 

93 

74 

35          81 

8.  510  7309 

243 

93 

78 

36          77 

8.  510  7296 

269 

94 

81 

37          73 

83 

294 

94 

85 

38          69 

70 

319 

94 

88 

39          64 

58 

345 

95 

92 

40  j   8.  509  0760 

X.510  7245 

1.35370 

2.  3895 

6.1395        7.861 

41  1         56 

32 

395 

95 

6.1399 

42 

52 

19 

420 

96 

6.  1403 

43 

47 

8.510  7207 

446 

96 

06 

44 

43 

8.  510  7194 

471 

% 

10 

45 

39 

81 

496 

97 

13 

46 

35 

68 

522 

97 

17 

47 

30 

55 

547 

97 

20 

48 

26 

43 

572 

97 

24 

49 

22 

30 

597 

98 

28 

50 

S.509  071* 

8.510  7117 

1.35623 

2.  3898 

6.  1431 

51 

13 

8.  510  7104 

648 

98 

35 

63 

09 

8.  510  7091 

673 

98 

38 

53 

05 

79 

698 

99 

42 

54 

8.509  0700 

66 

723 

99 

46 

55 

8.  509  0696 

53 

749 

2.3899 

49 

'   56 

92 

40 

774 

2.3900 

53 

57 

88 

27 

799 

00 

56 

58 

83 

15 

824 

00 

60 

M 

79 

8.  510  7002 

850 

00 

63 

60 

8.509  0676 

8.  510  6989 

1.35875 

2.3901 

6.1467        7.860 

238 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  42°. 


Lat. 

log  A 
diff.l"-~0.07 

logB 
diff.l"=-0.21  d 

logC 
iff.  1"=  +0.4 

logD 
2  diff.l"=+0.00 

logE 
diff.l"=+0.06 

logF 
diff.lO'=-0.9 

o   / 
42  00 

8.  509  0675 

8.  510  6989% 

1.35875 

2.  3901 

<;.Ht>7 

7.860 

1 

71 

76 

900 

01 

71 

2 

66 

64 

925 

01 

74 

3 

62 

51 

951 

01 

78 

4 

58 

38 

1.35976 

02 

81 

05 

54 

26 

1.36001 

02 

85 

6 

49 

12 

026 

02 

89 

j 

45 

8.  510  6900 

052 

03 

92 

8 

41 

8.  510  6887 

077 

03 

96 

9 

36 

74- 

102 

03 

6.1499 

10 

8.5090632 

8.  510  6861 

1.36127 

2.3903 

6.  1503 

11 

28 

48 

152 

04 

07 

12 

24 

36 

178 

04 

10 

13 

19 

23 

203 

04 

14 

14 

15 

8.  510  6810 

228 

04 

17 

15 

11 

8.  510  6797 

253 

05 

21 

16 

07 

84 

278 

05 

25 

17 

8.  509  0602 

72 

304 

05 

28 

18 

8.  509  0598 

59 

329 

05 

32 

19 

94 

46 

354 

06 

35 

20 

8.  509  0590 

8.  510  6733 

1.36379 

2.3906 

ti.  1539 

7.858 

21 

86 

20 

404 

06- 

43 

22 

81 

8.  510  6707 

430 

06 

46 

23 

77 

8.  610  6695 

455 

07 

50 

24 

72 

82 

480 

07 

54 

25 

68 

69 

505 

07 

57 

"26 

64 

56 

530 

07 

61 

27 

60 

43 

556 

08 

64 

28 

55 

31 

581 

08 

68 

29 

51 

18 

606 

08 

72 

30 

8.  509  0547 

8.  510  6605 

1.36631 

2.  3908 

(>.  1575 

31 

43 

8.  510  6592 

656 

08 

79 

32 

38 

79 

682 

09 

83 

33 

34 

66 

707 

09 

86 

34 

30 

54 

732 

09 

90 

35 

25 

41 

757 

09 

93 

36 

21 

28 

782 

10 

6.  1597 

37 

17 

15 

808 

10 

(i.  1601 

38 

13 

8.  510  6502 

833 

10 

04 

39 

08 

8.510  6490 

858 

10 

08 

40 

8.5090504 

8.  510  6477 

1.36883 

2.3910 

(i.  1612 

7.856 

41 

8.  509  0500 

64 

908 

11 

15 

42 

8.  509  0496 

51 

934 

11 

19 

43 

91 

38 

959 

11 

22 

44 

87 

25 

1.36984 

11 

26 

45 

83 

13 

1.37009 

12 

30 

46  . 

78 

8.  510  6400 

034 

12 

33 

47 

74 

8.  510  6387 

059 

12 

37 

48 

70 

74 

085 

12 

41 

49 

66 

61 

110 

12 

44 

50 

8.509  0461 

8.  510  6348 

1.37135 

2.3913 

6.1648 

51 

57 

36 

160 

13 

52 

52 

53 

23 

185 

13 

55 

53 

48 

8.  510  6310 

210 

13 

69 

54 

44 

8.  510  6297 

235 

13 

63 

55 

40 

84 

261 

14 

66 

66 

36 

71 

286 

14 

70 

57 

31 

59 

311 

14 

73 

68 

27 

46 

336 

14 

77 

59 

23 

33 

361 

14 

si 

60 

8.  509  0419 

8.510  6220 

1.37386 

2.  3914 

6.1684 

7.854 

GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  43°. 


239 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.21 

logC 
cliff.  1"=  +0.42 

logD 
cliff.  1"=  +0.00 

log  E        log  F 
cliff.  1"=  +0.06  diff.lO'=-1.0 

o   / 
43  CO 

8.  509  0419 

8.510  6220 

1.37386 

2.  3914 

0.1684        7.854 

1 

14 

8.  510  6207 

412 

15 

88 

2 

10 

8.510  6195 

437 

15 

92 

3 

06 

82 

462 

15 

95 

4 

8.509  0401 

69 

487 

15 

6.1699 

05 

8.  509  0397 

56 

512 

15 

6.  1703 

6 

93 

43 

537 

16 

06 

7 

89 

30 

563 

16 

10 

8 

84 

17 

588 

16 

14 

9 

80 

8.510  6105 

613 

16 

17 

10 

8.509  0376 

8.  510  6092 

1.37638 

•1.  3916 

ti.  1721 

11 

71 

79 

663 

16 

25 

12 

67 

66 

688 

17 

28 

13 

63 

•   53 

713 

17 

32 

»14 

59 

40 

739 

17 

36 

15 

54 

28 

764 

17 

39 

16 

50 

15 

789 

17 

43 

17 

46 

8.  510  6002 

814 

17 

47 

18 

41 

8.  510  5989 

839 

18- 

50 

19 

37 

76 

864 

18 

>  54 

20 

8.509  0333 

8.510  5963 

1.37889 

_>.  3918 

6.1758        7.852 

21 

29 

50 

915 

18 

61 

22 

24 

38 

940 

18 

65 

23 

20 

25 

965 

18 

69 

24 

16 

8.  510  5912 

1.37990 

18 

72 

25 

12 

8.510  5899 

1.  38015 

19 

76 

26 

07 

86 

040 

19 

80 

27 

8.509  0303 

73 

065 

19 

83 

28 

8.5D9  0299 

60 

091 

19 

87 

29 

94 

48 

116 

19 

91 

30 

8.509  0290 

8.510  5835 

1.38141 

'2.  3919 

6.1795 

31 

86 

22 

166 

20 

6.  1798 

32 

82 

8.  510  5809 

191 

20 

6.1802 

33 

77 

8.510  57% 

216 

20   • 

06 

34 

73 

83 

241 

20 

09 

35 

69 

71 

266 

20 

13 

36 

64 

58 

292 

20 

17 

37 

60 

45 

i)17 

20 

20 

38 

56 

32 

342 

20 

24 

39 

52 

19 

367 

21 

28 

40    8.  509  0247 

8.  510  5706 

1.38392 

2.  3921 

C..1831        7.850 

41 

43 

8.  510  5693 

417 

21 

35 

42 

39 

81 

442 

21 

39 

43 

34 

68 

467 

21 

42 

44 

30 

55 

492 

21 

46 

45 

26 

42 

518 

21 

50 

46 

22 

29 

543 

21 

53 

47 

17 

16 

568 

22 

57 

48 

13 

8.  510  5603 

593 

22 

61 

49 

09 

8.  510  5591 

618 

22 

65 

50 

8.  509  0204 

8.  510  6578 

1.38643 

2.  3922 

H.  1868 

51 

8.509  0200 

65 

668 

22 

72 

52 

8.  509  0196 

52 

693 

22 

76 

53 

92 

39 

719 

22 

79 

54 

87 

26 

744 

22 

83 

55 

83 

13 

769 

22 

87 

56 

79 

8.  510  5501 

794 

23 

91 

57 

74 

8.  510  5488 

819 

23 

94 

58 

70 

75 

844 

23 

f>.  1898 

f>9 

66 

62 

869 

23 

6.1902 

60 

8.  509  0162 

8.  510  5449 

1.38894 

2.  3928 

6.1905        7;848 

240 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  44°. 


Lat. 

log  A 
diff.  1"--0.07 

logB 
cliff.  1"=-0.21 

logC 
diff.  1"  =  +0.42 

logD 
diff.  1"=  +0.00 

log  E        log  F 
diff.  1"=  +  0.06  diff.  10'  =1.2 

o   / 

44  00 

8.509  0162 

8.510  5449 

1.38894 

2.  3923 

6.  1905        7.  848 

1 

57  • 

36 

919 

23 

09 

2 

53 

23 

945 

23 

13 

3 

49 

8.510  5411 

970 

23 

17 

4 

44 

8.  510  5398 

1.38995 

23 

20 

05 

40 

85 

1.39020 

23 

24 

6 

36 

72 

045 

24 

28 

7 

31 

59 

070 

24 

31 

8 

27 

46 

095 

24 

35 

9 

23 

33 

120 

24 

39 

10 

8.509  0119 

8.  510  5320 

1.39145 

2.  3924 

6.1943 

11 

14 

8.  510  5307 

171 

24 

46 

12 

10 

8.  510  5295 

196 

24 

50 

13 

06 

82 

221 

24 

54 

14 

8.509  0102 

69 

246 

24 

58 

15 

8.  509  0097 

56 

271 

24 

61 

16 

93 

43 

296 

24 

,   65 

17 

89 

30 

321 

24 

69 

18 

84 

18 

346 

24 

72 

19 

80 

8.  510  5205 

371 

25 

76 

20 

8.  509  0076 

8.,  510  5192 

1  .  39396 

2.  3925 

6.  1980        7.  845 

21 

72 

79 

422 

25 

84 

22 

67 

66 

447 

25 

87 

23 

63 

53 

472 

25 

91 

24 

59 

40 

497 

25 

95 

25 

54 

28 

522 

25 

6.  1999 

26 

50 

15 

547 

25 

6.2002 

27 

46 

8.  510  5102 

572 

25 

06 

28 

42 

8.  510  5089 

597 

25 

10  - 

^9 

37 

76 

623 

25 

14 

30 

8.  509  0033 

8.  510  5063 

1.39648 

2.  3925 

6.2017 

31 

29 

50 

673 

25 

21 

32 

24 

37 

698 

25 

25 

33 

20 

25 

723 

25 

29 

34 

16 

8.  510  5012 

748 

25 

32 

35 

11 

8.510  4999 

773 

25 

36 

36 

07 

86 

798 

26 

40 

37 

8.509  0003 

73 

823 

26 

44 

38 

8.  508  9999 

60 

848 

26 

47 

39 

94 

47 

873 

26 

51 

40 

8.508  9990 

8.510  4935 

1.39898 

2.8326 

6.  2055        7.  843 

41 

86 

22 

924 

26 

59 

42 

81 

8.510  4909 

949 

26 

62 

43 

77 

8.  510  4896 

974 

26 

66 

44 

73 

83 

1  .  39999 

26 

70 

45 

69 

70 

1.40024 

26 

74 

46 

64 

57 

049 

26 

77 

47 

60 

44 

074 

26 

81 

48 

56 

32 

099 

26 

85 

49 

51 

19 

124 

26 

89 

.50 

8.508  WIT 

8.510  4806 

1.40149 

2.  3926 

6.  2092 

51 

43 

8.  510  4793 

174 

26 

6.2096 

52 

39 

80 

200 

26 

6.  2100 

53 

34 

67 

225 

26 

04 

54 

30 

54 

250 

26 

08 

55 

26 

41 

275 

26 

11 

56 

21 

29 

300 

26 

15 

57 

17 

16 

S25 

26 

19 

58 

13 

8.  510  4703 

350 

26 

23 

59 

09 

8.  510  4690 

375 

26 

27 

60. 

8.508  9904 

8.  510  4677 

1.40400 

2.  3926 

6.  2130        7.  840 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  45°. 


241 


Lat. 

log  A 
diff.  1"  =  -  0.07 

logB 
diff.  1"=  -0.21 

logC 
diff.  1"=+0.42 

logD 
diff.  1"=  ±0.00  diff. 

logE 
1"=+0.06 

logF 
diff.lO'  =  -1.3 

o   / 

45  00 

8.508  9904 

8.510  4677 

1.40400 

2.3926 

6.2130 

7.840 

1 

8.508  9900 

64 

425 

26 

34 

2 

8.508  9896 

61 

450 

26 

38 

3 

91 

39 

475 

26 

42 

4 

87 

26 

501 

26 

46 

05 

83 

13 

526 

26 

49 

6 

78 

8.510  4600 

551 

26 

53 

7 

74 

8.  510  4587 

576 

26 

57 

8 

70 

74 

601 

26 

61 

9 

66 

61 

626 

26 

64 

10 

8.  508  9861 

8.510  4548 

1.40651 

2.  3926 

6.2168 

11 

57 

36 

676 

26 

72 

12 

53 

23 

.  '     701 

26 

76 

13 

48 

8.  510  4510 

727 

26 

80 

14 

44 

8.510  4497 

752 

26 

83 

15 

40 

8* 

777 

26 

87 

16 

36 

71 

802 

26 

91 

17 

31 

59 

827 

26 

95 

18 

27 

46 

852 

26 

6.2199 

19 

23 

33 

877 

26 

6.  2202 

20 

8.508  9818 

8.5104420 

1.40902 

2.  3926 

6.2206 

7.838 

21 

14 

8.  510  4407 

927 

26 

10 

22 

10 

8.  510  4394 

952 

26 

14 

23 

06 

81 

1.40978 

26 

18 

24 

8.  508  9801 

68 

1.41003 

26 

21 

25 

8.  508  9797 

56 

028 

26 

25 

26 

93 

43 

053 

26 

29 

27 

88 

3f 

078 

26 

33 

28 

84 

IV 

103 

26 

37 

29 

80 

8.510  4304 

128 

26 

40 

30 

8.508  9776 

8.  510  4291 

1.41153 

2.  3926 

6.2244 

31 

71 

78 

178 

26 

48 

32 

67 

65 

203 

26 

52 

33 

63 

52 

229 

26 

56 

34 

58 

40 

254 

26 

60 

35 

54 

27 

279 

26 

63 

36 

50 

14 

30-1 

25 

67 

37 

46 

8.  510  4201 

329 

25 

71 

38 

41 

8.510  4188 

354 

25 

75 

39 

37 

75 

379 

25 

79 

40 

8.  508  9733 

8.510  4162 

1.41404 

2.  3925 

0.  2283 

7.835 

41 

28 

49 

429 

25 

86 

42 

24 

37 

454 

25 

90 

43 

20 

24 

479 

25 

94 

44 

16 

8.510  4111 

505 

25 

6.  2298 

45 

11 

8.  510  4098 

530 

25 

6.  2302 

46 

07 

85 

555 

25 

06 

47 

8.  -508  9703 

72 

580 

25 

09 

48 

8.  508  9698 

60 

005 

25 

13 

49 

94 

17 

630 

25 

17 

50 

8.508  9689 

8.  510  4034 

1.  '11  055 

2.  3925 

6.  2321 

51 

85 

21 

68J 

25 

25 

52 

81 

8.510  4008 

705 

25 

29 

53 

77 

8.  510  3995 

731 

25 

32 

54 

72 

82 

756 

24 

36 

56 

68 

69 

781 

24 

40 

56 

64 

57 

800 

24 

44 

57 

60 

44 

831 

24 

48 

58 

55 

31 

856 

24 

52 

59 

51 

18 

881 

24 

55 

60 

8.  508  9647 

8.  510  3905 

1.41906 

2.  3924 

6.2359 

7.832 

4(KH)1—  08- 


-16 


242 


GEOGEAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  46°. 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.  1"=  -0.21 

logC 
diff.  1"=  +0.42 

logD 
diff.  V'=  -0.00 

log  E        log  F 
diff.  1"=  +0.06  diff.  10'=  -1.1 

o   / 

46  00 

8.  5C8  9647 

8.  510  3905 

1.41906 

2.  3924 

6.  2359        7.  832 

1 

43 

8.510  3892 

931 

24 

63 

2 

38 

79 

957 

24 

67 

3 

34 

67 

1.  41982 

24 

71 

4 

30 

54 

1.42007 

24 

75 

05 

25 

41 

032 

24 

79 

6 

21 

28 

057 

23 

82 

7 

17 

15 

082 

23 

86 

8 

13 

8.  510  3802 

107 

23 

90 

9 

08 

8.  510  3789 

132 

23 

94 

10 

8.  508  9604 

8.  510  3776 

1.42157 

2.  3923 

6.  2398 

11 

8.  508  9600 

64 

183 

23 

•  6.2402 

12 

8.  508  9595 

51 

208 

23 

06 

13 

91 

38 

233 

23 

09 

14 

87 

25 

258 

23 

13 

15 

83 

8.  510  3712 

283 

23 

17 

16 

78 

8.  510  3699 

308 

23 

21 

17 

74 

86 

333 

22 

25 

18 

70 

74 

358 

22 

29 

19 

65 

61 

384 

22 

33 

20 

8.  508  9561 

8.  510  13648 

1.42409 

2.3922 

6.  2436        7.  830 

21 

57 

35 

434 

22 

40 

22 

53 

22 

459 

22 

44 

23 

48 

8.  510  3609 

484 

22 

48 

24 

44 

8.  510  3596 

509 

22 

52 

25 

40 

84 

534 

22 

56 

26 

35 

71 

559 

21 

60 

27 

31 

58 

584 

21 

64 

28 

27 

45 

610 

21 

67 

29 

23 

32 

635 

21 

71 

30 

8.508  9518 

8.510  3519 

1.  42660 

2.  3921 

6.  2475 

31 

14 

8.  510  3506 

685 

21 

79 

32 

10 

8.  510  3494 

710 

21 

83 

33 

05 

81 

735 

21 

87 

34 

8.  508  9501 

68 

760 

20 

91 

35 

8.  508  9497 

55 

786 

20 

95 

36 

93 

42 

811 

20 

6.  2499 

37 

88 

29 

836 

20 

6.  2502 

38 

84 

17 

861 

20 

06 

39 

80 

8.  510  3404 

886 

20 

10 

40 

8.  508  9475 

8.  510  3391 

1.42911 

2.  3920 

6.2514        7.827 

41 

71 

78 

936- 

19 

18 

42 

67 

65 

961 

19 

22 

43 

63 

52 

1.  42987 

19 

26 

44 

58 

39 

1.43012 

19 

30 

45 

54 

27 

037 

19 

34 

46 

50 

14 

062 

19 

38 

47 

45 

8.  510  3301 

087 

19  • 

41 

48 

41 

8.  510  3288 

112 

18 

45 

49 

37 

75 

137 

18 

49 

50 

8.  508  9433 

8.  510  3262 

1.43163 

2.  3918 

6.  2553 

51 

28 

49 

188 

18 

57 

52 

24 

37 

213 

18 

61 

53 

20 

24 

238 

18 

65 

54 

16 

8.510  3211 

263 

18 

69 

55 

11 

8.  510  3198 

288 

17 

73 

56 

07 

85 

314 

17 

77 

57 

8.  508  9403 

72 

339 

17 

81 

58 

8.  508  9398 

60 

364 

17 

84 

59 

94 

47 

389 

17 

88 

60 

8.  508  9390 

8.  510  3134 

1.43414 

2.  3917 

6,  2592        7.  824 

GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  47°. 


243 


Lat. 

log  A 
diff.  1"=  -0.07 

logB 
diff.  1"=  -0.21 

logC 
d  iff.  1"=  +0.42 

logD 
diff.  1"=  -0.00 

log  E        log  F 
diff.  1"=  +0.07  diff.  10'  =  -1.6 

o   / 

47  00 

8.508  9390 

8.  510  3134 

1.  43414 

•2.  3917 

6.  2592        7.824 

1 

86 

21 

439 

16 

6.  25% 

2 

81 

8.  510  3108 

465 

16 

6.2600 

3 

77 

8.510  3095 

490 

16 

04 

4 

73 

82 

515 

16 

08 

05 

68 

70 

540 

16 

12 

6 

64 

57 

565 

16 

16 

7 

60 

44 

590 

15 

20 

8 

56 

31 

615 

15 

24 

9 

51 

18 

641 

15 

28 

10 

8.  508  9347 

8.  510  3005 

1.43666 

2.  3915 

6.  2632 

11 

43 

8.  510  2993 

691 

15 

35 

12 

38 

80 

716 

14 

39 

13 

34 

67 

741 

14 

43 

14 

30 

54 

766 

14 

47 

15 

26 

41 

792 

14 

51 

16 

21 

28 

817 

14 

55 

17 

17 

16 

842 

13 

59 

18 

13 

8.  510  2903 

867 

13 

63 

19 

09 

8.510  2890 

892 

13 

67 

20 

8.5089304 

8.510  2877 

1.43917 

2.3913 

G.  2671        7.  821 

21 

8.  508  9300 

64 

943 

13 

75 

22 

8.508  9296 

51 

968 

12 

79 

23 

91 

39 

1.43993 

12 

83 

24 

87 

26 

1.44018 

12 

87 

25 

83 

13 

043 

12 

91 

26 

79 

8.  510  2800 

069 

12 

95 

27 

74 

8.  510  2787 

094 

11 

6.  2699 

28 

70 

74 

119 

11 

6.  2702 

29 

66 

62 

144 

11 

06 

30 

8.  508  9261 

8.510  2749 

1.44169 

2.3911 

6.  2710 

31 

57 

36 

195 

11 

14 

32 

53 

23 

220 

10 

18   - 

33 

49 

8.510  2710 

245 

10 

22 

34 

44 

8.  510  2698 

270 

10 

26 

35 

40 

85 

295 

10 

30 

36 

36 

72 

321 

10 

34 

37 

32 

59 

346 

09 

38 

38 

27 

46 

371 

09 

42 

39 

23 

33 

396 

09 

46 

40 

8.  508  9219 

8.  510  2621 

1.44421 

2.3909 

6.2750        7.817 

41 

14 

8.510  2608 

447 

08 

54 

42 

10 

8.5102595 

472 

08 

58 

43 

06 

82 

497 

08 

62 

44 

8.  508  9202 

69 

522 

08 

66   • 

45 

8.  508  9197 

57 

547 

07 

70 

46 

93 

44 

673 

07 

74 

47 

89 

31 

598 

07 

78 

48 

84 

18 

623 

07 

82 

49 

80 

8.510  2505 

648 

07 

86 

50 

8.508  9176 

8.  510  2493 

1.44673 

2.3906 

6.2790 

51 

72 

80 

699 

06 

94 

52 

67 

67 

724 

06 

6.  2798 

53 

63 

54 

749 

06 

6.2802 

54 

59 

41 

774 

05 

06 

55 

55 

28 

800 

05 

10 

56 

50 

16 

825 

05 

14 

57 

46 

8.510  2403 

850 

05 

18 

58 

42 

8.510  2390 

875 

04 

22 

59 

38 

77 

900 

04 

26 

60 

8.  508  9133 

8.  510  2364 

1  .  44926 

2.  3904 

6.2830        7.814 

244 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  48°. 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.21 

logC 

logD 
2  diff.l";  0.00 

logE 
diff.l"=+0.07  diff. 

logF 
10'—  1.7 

o   / 
48  00 

8.5089133 

8.510  2364 

1.44926 

2.3904 

6.2830 

7.814 

1 

29 

52 

951 

04 

34 

2 

25 

39 

1.44976 

03 

38 

3 

20 

26 

1.45001 

03 

42 

4 

16 

13 

027 

03 

46 

05 

12 

8.  510  2300 

052 

02 

50 

6 

08 

8.  510  2288 

077 

02 

54 

7 

8.  508  9103 

75 

102 

02 

58 

8 

8.  508  9099 

62 

128 

02 

62 

9 

95 

49 

153 

01 

66 

10 

8.  508  9091 

8.510  2236 

1.45178 

2.3901 

6.2870 

11 

86 

24 

203 

01 

74 

12 

82 

8.  510  2211 

229 

01 

78 

13 

78 

8.  510  2198 

254 

00 

82 

14 

74 

85 

279 

00 

86 

15 

69 

72 

304 

2.3900 

90 

16 

65 

60 

330 

2.3899 

94 

17 

61 

47 

355 

99 

6.2898 

18 

57 

34 

380 

99 

6.2902 

19 

52 

21 

406 

99 

06 

20 

8.508  9048 

8.  510  2108 

1.45431 

2.  3898 

6.2910 

7.811 

21 

44 

8.  510  2096 

456 

98 

14 

22 

39 

83 

481 

98 

18 

23 

35 

70 

507 

97 

22 

24 

31 

57 

532 

97 

26 

25 

27 

45 

557 

97 

30 

26 

22 

32 

582 

97 

34 

27 

18 

19 

608 

96 

38 

28 

14 

8.  510  2006 

633 

96 

42 

29 

10 

8.510  1993 

658 

96 

46 

30 

8.  508  9005 

S.510  1981 

1.45683 

2.  3895 

6.2950 

31 

8.  508  9001 

68 

709 

95 

54 

32 

8.508  8997 

55 

734 

95 

58 

33 

93 

42 

759 

95 

62 

34 

88 

30 

785 

94 

66 

35 

84 

17 

810 

94 

70 

36 

80 

8.510  1901 

835 

94 

74 

37 

76 

8.510  1891 

861 

93 

78 

38 

71 

78 

886 

93 

82 

39 

67 

66 

911 

93 

86 

40 

8.  508  8963 

8.510  1853 

1.45937 

2.  3892 

6.2990 

7.807 

41 

59 

40 

982 

92 

94 

42 

54 

27 

1.45987 

92 

6.  2998 

43 

50 

15 

1.46012 

91 

6.3002 

44 

46 

8.510  1802 

038 

91 

06 

45 

41 

8.510  1789 

063 

91 

10 

46 

37 

76 

088 

90 

15 

47 

33 

64 

.  114 

90 

19 

48 

29 

51 

189 

90 

23 

49 

24 

38 

164 

89 

27 

50 

8.508  8920 

8.510  172"! 

1.46190 

2.3889 

6.3031 

51 

16 

13 

215 

89 

35 

52 

12 

8.510  1700 

240 

88 

39 

53 

08 

8.510  1687 

266 

88 

43 

54 

8.  508  8903 

74 

291 

88 

47 

55 

8.  508  8899 

62 

316 

87 

51 

56 

95 

49 

342 

87 

55 

57 

90 

36 

367 

87 

59 

58 

86 

23 

392 

86 

63 

59 

82 

8.510  1610 

418 

86 

67 

60 

8.508  8878 

8,510  1598 

1  .  46443 

2.3886 

6.3071 

7.804 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  49°. 


245 


Lat. 

log  A 
diff.  1"=  -0.07 

logB 
diff  .  1"=  -0.21 

logC 
diff.  1"  =+0.42 

logD 
diff.  1"=  -0.01 

log  E        log  F 
d  iff.  1"=+  0.07  diff.  10'=  -1.9 

o   / 
49  00 

8.  508  8878 

8.510  1598 

1.46443 

2.3886 

6.  3071        7.  804 

1 

73 

85 

468 

85 

75 

2 

69 

72 

494 

85 

79 

3 

65 

59 

519 

85 

84 

4 

61 

47 

544 

84 

88 

05 

57 

34 

570 

84 

92 

6 

52 

21 

595 

84 

6.30% 

7 

48 

8.510  1508 

621 

83 

6.  3100 

8 

44 

8.510  14% 

646 

83 

04 

9 

39 

83 

671 

83 

08 

10 

8.508  8835 

8.510  1470 

1.466% 

•2.  3882 

6.3112 

11 

31 

58 

722 

82 

16 

12 

27 

45 

747 

81 

20 

13 

23 

32 

773 

81 

24 

14 

18 

19 

798 

81 

28 

15 

14 

8.510  1407 

824 

80 

32 

16 

10 

8.  510  1394 

849 

80 

37 

17 

06 

81 

-  874 

80 

41 

18 

8.508  8801 

68 

899 

79 

45 

19 

8.  508  8797 

56 

925 

79 

49 

20 

8.  508  8793 

8.510  1343 

1.46950 

2.  3878 

6.3153        7.800 

21 

89 

30 

1.46976 

78 

57 

22 

84 

17 

1.47001 

78 

61 

23 

80 

8.510  1305 

026 

77 

65 

24 

76 

8.  510  1292 

052 

77 

69 

25 

72 

79 

077 

77 

73 

26 

67 

67 

103 

76 

78 

27 

63 

54 

128 

76 

82 

28 

59 

41 

153 

75 

86 

29 

55 

28 

179 

75 

90 

30 

8.  508  8750 

8.510  1216 

1.47204 

2.3875 

6.3194 

31 

46 

8.510  1'203 

230 

74 

6.3198 

32 

42 

8.510  1190 

255 

74 

(I.  *202 

33 

38 

78 

281 

73 

06 

34 

33 

65 

306 

73 

10 

35 

29 

52 

331 

73 

15 

36 

25 

39 

357 

72 

19 

37 

21 

27 

382 

72 

23 

38 

16 

14 

408 

71 

27 

39 

12 

8.510  1101 

433 

71 

31 

40 

8.  508  8708 

8.510  1088 

1.47459 

2.  3871 

6.  3235        7.  796 

41 

04 

76 

484 

70 

39 

42 

8.  508  8700 

63 

509 

70 

43 

43 

8.508  8695 

50 

535 

69 

47 

44 

91 

38 

560 

69 

52 

45 

87 

25 

586 

69 

56 

46 

83 

12 

611 

68 

60 

47 

78 

8.510  1000 

637 

68 

64 

48 

74 

8.  510  0987 

662 

67 

68 

49 

70 

74 

688 

67 

72 

50 

8.508  8666 

8.510  0962 

1.47713 

2.3866 

6.  3276 

51 

61 

49 

738 

66 

81 

52 

57 

36 

764 

66 

85 

53 

53 

23 

789 

65 

89 

54 

49 

8.510  0911 

815 

65 

93 

55 

45 

8.510  0898 

840 

64 

6.  3297 

56 

40 

85 

866 

64 

6.3301 

57 

36 

73 

891 

63 

05 

58 

32 

60 

917 

63 

09 

59 

28 

48 

942 

63 

14 

CO 

8.  508  8623 

8.  510  0835 

1.47968 

2.3862 

6.3318        7.792 

246 


GEOGRAPHIC    TABLES    AND  FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  50°. 


Lat. 

log  A 
diff.  l"=  -0.07 

logB 
diff.  1"=  -0.21 

logC 
diff.  1"-  +0.43 

logD 
diff  1"=  -0.01  diff. 

logE 
1"-+0.07  diff. 

logF 
10'  =  -2.0 

o   / 
50  00 

8.  508  8623 

8.  510  0835 

1.  47968 

2.3862 

6.  3318 

7.  792 

1 

19 

22 

1.47993 

62 

22 

2 

15 

8.  510  0809 

1.  48019 

61 

26 

3 

11 

8.  510  0797 

044 

61 

30 

4 

06 

84 

070 

60 

34 

05 

8.  508  8602 

71 

095 

60 

39 

6 

8.  508  8598 

59 

121 

60 

43 

7 

94 

46 

146 

59 

47 

8 

90 

33 

172 

59 

51 

9 

85 

21 

197 

58 

55 

10 

8.  508  8581 

8.  510  0708 

1.48223 

2.  3858 

6.  3359 

11 

77 

8.  510  0695 

248 

57 

63 

12 

73 

83 

274 

57 

68 

13 

68 

70 

299 

56 

72 

14 

64 

57 

325 

56 

76 

15 

60 

45 

350 

55 

80 

16 

56 

32 

376 

55 

84 

17 

52 

19 

401 

65 

88 

18 

47 

8.  510  0607 

427 

54 

93 

19 

43 

8.  510  0594 

452 

54 

6.  3397 

20 

8.  508  8539 

8.  510  0581 

1.48478 

2.3863 

6.  3401 

7.788 

21 

35 

69 

504 

53 

06 

22 

30 

66 

529 

52 

09 

23 

26 

43 

555 

52 

14 

24 

22 

31 

680 

51 

18 

25 

18 

18 

606 

51 

22 

26 

14 

8.  510  0505 

631 

60 

26 

27 

09 

8.  510  0493 

657 

50 

30 

28 

05 

80 

682 

49 

34 

29 

8.508  8601 

67 

708 

49 

39 

30 

8.  508  8497 

8.  510  0455 

1  48734 

2.3848 

6.  3443 

31 

93 

42 

759 

48 

47 

32 

88 

29 

786 

47 

51 

33 

84 

17 

810 

47 

55 

34 

80 

8.  510  0404 

836 

46 

60 

35 

76 

8.  510  0392 

861 

46 

64 

36 

71 

79 

887 

45 

68 

37 
38 

67 
63 

R 

913 

938 

45 
44 

72 

76 

39 

59 

41 

964 

44 

81 

40 

8.  508  8455 

8  510  0328 

1.48989 

2.  3843 

6.  3485 

7.784 

41 

50 

16 

1  49015 

43 

89 

42 

46 

8  510  0303 

041 

42 

93 

43 

42 

8.510  0291 

066 

42 

6  3497 

44 

38 

78 

092 

41 

6.3502 

45 

34 

65 

117 

41 

06 

46 

29 

53 

143 

40 

10 

47 

25 

40 

169 

40 

14 

48 

21 

27 

194 

39 

18 

49 

17 

15 

2-20 

39 

23 

50 

8.508  8413 

8.510  0202 

1  .  49246 

2.  383S 

6.  3527 

•  51 

08 

8.510  0190 

271 

38 

31 

52 

04 

77 

297 

37 

35 

53 

8.  508  8400 

64 

322 

37 

40 

54 

8.  508  8396 

52 

348 

36  , 

44 

55 

92 

39 

374 

36 

48 

56 

87 

27 

399 

35 

52 

57 

83 

14 

425 

35 

56 

58 

79 

8.510  0101 

451 

34 

61 

59 

75 

8.510  0089 

476 

34 

65 

60 

8.508  8371 

8.510  0076 

1.49502 

2.3833 

6.3569 

7.780 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  51°. 


247 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.21 

logC 
diff.l"=+0.43 

logD 
diff.l"=-0.01 

Jog  E        log  F 
diff.  1"  =  +0.07  diff.lO'=~2.2 

O    ' 

51  00 

8.508  8371 

8.510  0076 

1.49502 

2.3833 

6.  3569        7.  780 

1 

66 

64 

528 

33 

73 

2 

62 

51 

553 

32 

78 

3 

58 

38 

579 

32 

82 

4 

54 

26 

605 

31 

86 

05 

50 

13 

630 

31 

90 

6 

45 

8.510  0001 

656 

30 

95 

7 

41 

8.  509  9988 

682 

29 

6.3599 

8 

37 

75 

707 

29 

6.  3603 

9 

33 

63 

733 

28 

07 

10 

8.  508  8329 

8.  509  9950 

J  .  49759 

2.3828 

6.  3612 

11 

24 

38 

785 

27 

16 

12 

20 

25 

810 

27 

20 

13 

16 

13 

836 

26 

24 

14 

VI 

8.  509  9900 

862 

26 

28 

15  |         08 

8.  509  9887 

887 

25 

33 

16 

8.  508  8303 

75 

913 

25 

37 

17 

8.508  8299 

62 

939 

24 

41 

18 

95 

50 

965 

23 

45 

19 

91 

37 

1.49990 

2& 

50 

20 

8.  508  8287 

8.509  9825 

1.50016 

2.3822 

6.  3654        7.  776 

21 

82 

8.  509  9812 

042 

22 

58 

2-2 

78 

8.  509  9799 

067 

21 

63 

23 

74 

87 

093 

21 

67 

24 

70 

74 

119 

20 

71 

25 

66 

62 

145 

20 

75 

26 

62 

49 

170 

19 

80 

27 

67 

37 

1% 

18 

84 

28 

53 

24 

222 

18 

88 

29 

49 

8.509  9711 

248 

17 

92 

30 

8.  508  8245 

8.  509  9699 

1.50273 

2.3817 

6.  3697 

31 

41 

86 

299 

16 

6.  3701 

32 

36 

74 

325 

16 

05 

33 

32 

61 

351 

15 

10 

34 

28 

49 

376 

14 

14 

35 

24 

36 

402 

14 

18 

36 

20 

24 

428 

13 

22 

37 

16 

8.509  9611 

454 

13 

27 

38 

11 

8.509  9599 

480 

12 

81 

39 

07 

86 

505 

11 

35 

40 

8.  508  8203 

8.  509  9574  , 

1.50531 

2.3811 

6.  3740        7.  772 

41 

8.508  8199 

61 

557 

10 

44 

42 

95 

48 

583 

10 

48 

43 

90 

36 

609 

09 

52 

44 

86 

23 

634 

08 

57 

45 

82 

8.  509  9511 

660 

08 

61 

46 

78 

8.509  9498 

686 

07 

65 

47 

74 

86 

712 

07 

70 

48 

70 

73 

738 

06 

74 

49 

65 

61 

764 

05 

78 

50 

8.  508  8161 

8.  509  9448 

1.50789 

2.3805 

6.  3782 

51 

57 

36 

815 

04 

87 

52 

53 

23 

841 

04 

91 

53 

49 

8.  509  9411 

867 

03 

6.  3795 

54 

45 

8.  509  9398 

893 

02 

6.3800 

55 

40 

86 

919 

02 

04 

56 

36 

73 

944 

01 

08 

57 

32 

61 

970 

01 

13 

58 

28 

48 

1.50996 

2.3800 

17 

59 

24 

36 

1.51022 

2.  3799 

21 

60 

8.  508  8120 

8.  509  9323 

1.51048 

2.  3799 

6.  3826        7.  767 

248 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  52°. 


Lat. 

log  A 
diff.l"--0.07 

logB 
diff.l"=-0.21 

logC 
diff.l"=+0.43 

logD 
diff.l"=-0.01  d 

log  E        log  F 
iff.  l"  =  -f  0.07  diff.10'^-2.3 

r>   / 
52  00 

8.  508  8120 

8.  509  9323 

1.51048 

2.  3799 

6.  3826        7.  767 

1 

15 

8.509  9311 

074 

98 

30 

2 

11 

8.  509  9298 

100 

97 

34 

3 

07 

86 

126 

97 

39 

4 

8.  508  8103 

73 

151 

96 

43 

05 

8.  508  8099 

61 

177 

96 

47 

6 

95 

48 

203 

95 

52 

7 

90 

36 

229 

94 

56 

8 

86 

23 

255 

94 

60 

9 

82 

8.509  9211 

281 

93 

65 

10 

8.  508  8078 

8.509  9198 

1.51307 

2.  3792 

6.3869 

11 

74 

86 

333 

92 

73 

12 

70 

73 

359 

91 

78 

13 

65 

61 

385 

91 

82 

14 

61 

48 

411 

90 

86 

15 

57 

36 

436 

89 

91 

16 

53 

23 

462 

88 

95 

17 

49 

8.509  9111 

488 

88 

6.3899 

18 

45 

8.509  9099 

514 

87 

6.3904 

19 

41 

86 

640 

87 

08 

20 

8.  508  8036 

8.  509  9074 

1.51566 

2.3786 

6.  3912        7.  763 

21 

32 

61 

592 

85 

17 

22 

28 

49 

618 

85 

21 

23 

24 

36 

644 

84 

25 

24 

20 

24 

670 

83 

30 

25 

16 

8.509  9011 

696 

83 

34 

26 

11 

8.  509  8999 

722 

82 

38 

27 

07 

86 

748 

81 

43 

28 

8.  508  8003 

74 

774 

81 

47 

29 

8.  508  7999 

62 

800 

80 

51 

30 

8.508  7995 

8.  509  8949 

1.  51826 

2.  3779 

6.3956 

31 

91 

37 

852 

79 

60 

32 

87 

24 

878 

78 

66 

33 

82 

8.509  8912 

904 

78 

69 

34 

78 

8.509  8899 

930 

77 

73 

35 

74 

87 

956 

76 

78 

36 

70 

74 

1.51982 

75 

82 

37 

66 

62 

1.52008 

75 

86 

38 

62 

50 

034 

74- 

91 

39 

58 

37 

060 

73 

6.  3995 

40 

8.  508  7953 

8.509  8825 

1.52086 

2.3773 

6.4000       7.758 

41 

49 

12 

112 

72 

04 

42 

45 

8.509  8800 

138 

.  71 

08 

43 

41 

8.  509  8788 

164 

71 

13 

44 

37 

75 

190 

70 

17 

45 

33 

63 

216 

69 

21 

46 

29 

50 

242 

68 

26 

47 

24 

38 

268 

68 

30 

48 

20 

25 

294 

67 

35 

49 

16 

13 

320 

66 

39 

50 

8.508  7912 

8.  509  8701 

1.52347 

2.3766 

7.4043 

51 

08 

8.  509  8688 

373 

65 

48 

52 

04 

76 

399 

64 

52 

53 

8.508  7900 

63 

425 

64 

67 

54 

8.508  7895 

51 

451 

63 

61 

55 

91 

39 

477 

62 

65 

56 

87 

26 

5C3 

61 

70 

57 

83 

14 

529 

61 

74 

58 

79 

8.509  8602 

555 

60 

79 

59 

75 

8.509  8589 

581 

59 

83 

60 

8.508  7871 

8.509  8577 

1.52608 

2.  3759 

6.  4088        7.  753 

GEOGRAPHIC   TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  53°. 


249 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"=-0.21 

logC 
diff.l"=  +0.44 

logD 
diff.l"=-0.01 

logE 
diff.l"  -+0.07 

diff.lO'=-2.5 

o   / 

53  00 

8.508  7871 

8.  509  8577 

1.52608 

2.  3759 

6.4088 

7.  753 

1 

67 

64 

634 

58 

92 

2 

62 

52 

660 

57 

6.4096 

3 

58 

40 

686 

56 

6.  4101 

4 

54 

27 

712 

56 

05 

05 

50 

15 

738 

55 

10 

6 

46 

8.509  8502 

764 

54 

14 

7 

42 

8.  509  8490 

790 

53 

18 

8 

38 

78 

817 

53 

28 

9 

34 

65 

843 

52 

27 

10 

8.  508  7829 

8.  509  8453 

•1.52869 

2.3751 

6.4132 

11 

25 

41 

895 

51 

36 

12 

21 

28 

921 

50 

41 

13 

17 

16 

947 

49 

45 

14 

13 

8.509  8404 

1.52974 

48 

49 

15 

09 

8.  509  8391 

1.53000 

48 

54 

16 

"  05 

79 

026 

47 

58 

17 

8.  508  7801 

67 

052 

46 

63 

18 

8.  508  7797 

54 

078 

45 

67 

19 

92 

42 

105 

45 

72 

20 

8.  508  7788 

8.509  8329 

1.53131 

2.  3744 

6.  4176 

7.748 

21 

84 

17 

157 

43 

80 

22 

80 

8.5098305 

183 

42 

85 

23 

76 

8.  509  8292 

209 

42 

89 

24 

72 

80 

236 

41 

94 

25 

68 

68 

262 

40 

6.  4198 

26 

64 

55 

288 

39 

6.4203 

27 

60 

43 

314 

39 

07 

28 

55 

31 

341 

38 

12 

29 

51 

18 

367 

37 

16 

30 

8.508  7747 

8.509  8206 

1.53393 

2.3736 

6.  4221 

31 

43 

8.  509  8194 

419 

36 

25 

32 

39 

82 

446 

35 

29 

33 

35 

69 

472 

34 

34 

34 

31 

57 

498 

33 

38 

35 

27 

46 

524 

33 

43 

36 

23 

32 

551 

32 

47 

37 

18 

20 

577 

31 

52 

38 

14 

8.509  8108 

603 

30 

56 

39 

10 

8.509  8095 

630 

29 

61 

40 

8.508  7706 

8.5098083 

1.53656 

2.3729 

6.4265 

7.743 

41 

8.508  7702 

71 

682 

28 

70 

42 

8.  508  7698 

58 

709 

27 

74 

43 

94 

46 

735 

26 

79 

44 

90 

34 

761 

26 

83 

45 

86 

22 

788 

25 

88 

46 

82 

8.509  8009 

814 

24 

92 

47 

77 

8.509  7997 

840 

23 

6.4297 

48 

73 

85 

867 

22 

6.4301 

49 

69 

72 

893 

22 

06 

50 

8.508  7665 

8.509  7960 

1.53919 

2.  3721 

6.  4310 

51 

61 

48 

946 

20 

15 

52 

57 

36 

972 

19 

19 

53 

53 

23 

1.53998 

18 

24 

54 

49 

8.509  7911 

1.54025 

18 

28 

55 

45 

8.  509  7899 

051 

17 

33 

56 

41 

87 

077 

16 

37 

57 

37 

74 

104 

15 

42 

58 

32 

62 

130 

14 

46 

59 

28 

•  60 

157 

14 

51 

60 

8.508  7624 

8.509  7838 

1.54183 

2.  3713 

6.4355 

7.738 

250 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  54°. 


Lat. 

log  A 
diff.  1"=-0.07 

logB 
diff.l"=-0.20 

logC 
diff.  1"=  +0.44 

logD 
diff.  1"=  -0.01 

logE 
diff.  1"=+0.08  diff 

logF 
10'=  -2.6 

o   / 
64  00 

8.508  7624 

8.509  7838 

1.54183 

2.3713 

6.  4355 

7.738 

1 

20 

25 

209 

12 

60 

2 

16 

13 

236 

11 

64 

3 

12 

8.  509  7801 

262 

10 

69 

4 

08 

8.509  7789 

288 

•  09 

73 

05 

04 

76 

315 

09 

78 

6 

8.  508  7600 

64 

341 

08 

82 

7 

8.  508  7596 

52 

368 

07 

87 

8 

92 

40 

394 

06 

91 

9 

88 

27 

421 

05 

6.  4396 

10 

8.  508  7584 

8.509  7715 

1.  54447 

2.  3705 

6.4400 

11 

79 

8.  509  7703 

474 

04 

05 

12 

75 

8.  509  7691 

500 

03 

09 

13 

71 

78 

527 

02 

14 

14 

67 

66 

553 

01 

18 

15 

63 

54 

580 

00 

23 

16 

59 

42 

606 

2.3700 

28 

17 

55 

30 

633 

2.  3699 

32 

18 

51 

17 

659 

98 

37 

19 

47 

8.509  7605 

686 

97 

41 

20 

8.  508  7543 

8.  509  7593 

1.54712 

2.  3696 

6.  4446 

7.733 

21 

39 

81 

739 

95  . 

50 

22 

35 

69 

765 

94 

55 

23 

31 

56 

792 

94 

59 

24 

27 

44 

818 

93 

64 

25 

22 

32 

845 

92 

68 

26 

18 

20 

871 

91 

73 

27 

14 

8.  509  7508 

898 

90 

78 

28 

10 

8.  509  7495 

924 

89 

82 

29 

06 

83 

951 

88 

87 

30 

8.508  7502 

8.  509  7471 

1.54977 

2.  3688 

6.  4491 

31 

8.  508  7498 

59 

1.55004 

•87 

6.  4496 

32 

94 

47 

031 

86 

6.4500 

33 

90 

34 

057 

85 

05 

34 

86 

22 

084 

84 

09 

35 

82 

8.509  7410 

110 

83 

14 

36 

78 

8.  509  7398 

137 

82 

19 

37 

74 

86 

163 

82 

23 

38 

70 

74 

190 

81 

28 

39 

66 

61 

217 

80 

32 

40 

8.508  7462 

8.509  7349 

1.55243 

2.  3679 

6.  4537 

7.728 

41 

58 

37 

270 

78 

41 

42 

53 

25 

297 

77 

46 

43 

49 

13 

323 

76 

51 

44 

45 

8.509  7301 

350 

75 

55 

45 

41 

8.509  7289 

376 

74 

60 

46 

37 

76 

403 

74 

64 

47 

33 

64 

430 

73 

69 

48 

29 

52 

456 

72 

74 

49 

25 

40 

483 

71 

78 

50 

8.  508  7421 

8.509  7228 

1.55510 

2.3670 

6.4583 

51 

17 

16 

536 

69 

87 

52 

13 

8.509  7204 

563 

68 

92 

53 

09 

8.509  7191 

590 

67 

6.  4597 

54 

05 

79 

616 

66 

6.  4601 

55 

8.  508  7401 

67 

643 

66 

06 

56 

8.  508  7397 

55 

670 

65 

10 

57 

93 

43 

696 

64 

15 

58 

89 

31 

723 

63 

20 

59 

85 

19 

750 

62 

24 

60 

8.  508  7381 

8.509  7107 

1.  55777 

2.3661 

6.4629 

7.723 

GEOGRAPHIC   TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  65°. 


251 


Lat. 

log:  A 
diff.  1"=  -0.07 

logB 
diff.l"=-0.20 

logC 
diff.  1"  +0. 

logD 
5  diff.  1"=-0.02 

log  E        log  F 
diff.l"-+O.CX  diff.iy=-2.8 

o   / 
55  00 

8.  508  7381 

8.  509  7107 

1.55777 

2.3661 

6.4629        7.723 

1 

77 

8.  509  7095 

803 

60 

33 

2 

73 

82 

830 

59 

38 

3 

69 

70 

857 

58 

43 

4 

65 

58 

884 

57 

47 

05 

61 

46 

910 

56 

52 

6 

56 

34 

937 

56 

57 

7 

52 

22 

964 

55 

61 

8 

48 

8.  509  7010 

1.  55991 

54 

€6 

9 

44 

8.509  6998 

1.56017 

53 

70 

10 

8.  508  7340 

8.509  6986 

1.56044 

2.3652 

6.  4675 

11 

36 

74 

071 

51 

80 

12 

32 

62 

098 

50 

84 

13 

28 

49 

125 

49 

89 

14 

24 

37 

151 

48 

94 

15 

20 

25 

178 

47 

6.  4698 

16 

16 

13 

205 

46 

6.  4703 

17 

12 

8.5096901 

232 

45 

08 

18 

08 

8.509  6889 

259 

44 

12 

19 

04 

77 

286 

43 

IV 

20 

8.508  7300 

8.  509  6865 

1.56312 

2.  3642 

6.  4721        7.  717 

21 

8.508  7296 

53 

339 

42 

26 

22 

92 

41 

366 

41 

31 

23 

88 

29 

393 

40 

35 

24 

84 

17 

420 

39 

40 

25 

80 

8.509  6805 

447 

38 

45 

26 

76 

8.  509  6793 

474 

37 

49 

27 

72 

81 

500 

36 

54 

28 

68 

69 

527 

35 

59 

29 

64 

57 

554 

34 

63 

30 

8.508  7260 

8.  509  6745 

1.56581 

2.  3633 

6.4768 

31 

56 

33 

608 

32 

73 

32 

52 

21 

635 

31 

77 

33 

48 

8.  509  6709 

662 

30 

82 

34 

44 

8.509  6696 

689 

29 

87 

35 

40 

84 

716 

28 

91 

36 

36 

72 

743 

27 

6.4796 

37 

32 

60 

770 

26 

6.4801 

38 

28 

48 

•   797 

25 

05 

39 

24 

36 

823 

24 

10 

40 

8.  508  7220 

8.509  6624 

I..r6850 

2.3623 

6.  4815        7.  711 

41 

16 

12 

877 

22 

20 

42 

12 

8.509  6600 

904 

21 

24 

43 

08 

8.509  6588 

931 

20 

29 

44 

04 

76 

958 

19 

34 

45 

8.  508  7200 

64 

1.56985 

18 

38 

46 

8.  508  7196 

52 

1.57012 

17 

43 

47 

92 

40 

039 

16 

48 

48 

88 

28 

066 

15 

52 

49 

84 

16 

093 

14 

57 

50 

8.  508  7180 

8.509  6505 

1.57120 

2.  613 

6.4862 

51 

76 

8.  509  6493 

147 

12 

66 

52 

72 

81 

174 

11 

71 

53 

68 

69 

201 

10 

76 

54 

64 

57 

229 

09 

81 

55 

60 

45 

256 

08 

85 

56 

56 

33 

283 

07 

90 

67 

52 

21 

310 

06 

6.  4895 

58 

48 

8.509  6409 

337 

06 

0.4900 

59 

44 

8.509  6397 

364 

04 

04 

60 

8.508  7140 

8.  509  6385 

1.57391 

2.  3603 

6.  4909        7.  706 

252 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  56°. 


Lat. 

log  A 
diff.l"=-0.07 

logB 
diff.l"  =  -0.20 

logC 
diff.l"=+0.45 

logD 
diff.l"  =  -0.02 

logE 
diff.l"  =  +0.0 

logF 
8  diff.lO'  =  -3.0 

o   / 
56  00 

S.  508  7140 

8.  509  6385 

1.  57391 

2.3603 

6.4909 

7.706 

1 

36 

73 

418 

02 

14 

2 

32 

61 

445 

01 

18 

3  - 

28 

49 

472 

2.3600 

23 

4 

24 

37 

499 

2.3599 

28 

05 

20 

25 

526 

98 

33 

6 

16 

13 

554 

97 

37 

7 

12 

8.  509  6301 

581 

96 

42 

8 

08 

8.  509  6289 

608 

95 

47 

9 

04 

77 

635 

94 

52 

10 

8.  508  7100 

8.  509  (J26C 

1.57662 

2.3593 

6.4956 

11 

8.  508  7096 

54 

689 

92 

61 

12 

92 

42 

717 

91 

66 

13 

88 

30 

744 

90 

71 

14 

84 

18 

771 

89 

75 

15 

80 

8.  509  6206 

798 

88 

80 

16 

76 

8.  509  6194 

825 

-87 

85 

17 

72 

82 

852 

86 

90 

18 

69 

70 

880 

85 

94 

19 

65 

58 

907 

84 

0.  4999 

20 

8.  508  7061 

8.509  (147 

1.  57934 

2.3583 

C>.  .5004 

7.700 

21 

57 

35 

961 

82 

09 

22 

53 

23 

1.  57989 

81 

13 

23 

49 

8.509  6111 

1.58016 

80 

18 

24 

45 

8.509  6099 

043 

78 

23 

26 

41 

87 

070 

77 

28 

26 

37 

75 

098 

76 

32 

27 

33 

63 

125 

75 

37 

28 

29 

51 

152 

74 

42 

» 

29 

25 

40 

179 

73 

47 

30 

8.  508  7021 

8.  509  6028 

1.58207 

2.3572 

6.5052 

31 

17 

16 

234 

71 

56 

32 

13 

8.509  6004 

261 

70 

61 

33 

09 

8.509  5992 

289 

69 

66 

34 

05 

80 

316 

68 

71 

35 

8.508  7001 

68 

343 

67 

75 

36 

8.  508  6997 

57 

371 

66 

80 

37 

93 

45 

398 

65 

85 

38 

89 

33 

425 

64 

90 

39 

86 

21 

453 

62 

95 

40 

8.  508  6982 

8.509  5909 

1.58480 

2.3561 

6.5099 

7.694 

41 

78 

8.  509  5897 

507 

60 

6.5104 

42 

74 

86 

535 

59 

09 

43 

70 

74 

562 

58 

14 

44 

66 

62 

589 

57 

19 

45 

62 

50 

617 

56 

24 

46 

58 

38 

644 

55 

28 

47 

54 

27 

672 

54 

33 

48 

50 

15 

699 

53 

38 

49 

46 

8  509  5803 

726 

52 

43 

50 

8.  508  6942 

8.509  5791 

1.58754 

2.3550 

6.5148 

51 

38 

79 

781 

49 

52 

52 

34 

67 

809 

48 

57 

.  53 

30 

56 

836 

47 

62 

54 

26 

44 

864 

46 

67 

55 

23 

32 

891 

45 

72 

56 

19 

20 

919 

44 

77 

57 

15 

8.  509  5709 

946 

43 

81 

58 

11 

8.  509  5697 

1.58974 

42 

86 

59 

07 

85 

1.59001 

41 

91 

60 

8.508  6903 

8.509  5673 

1.59028 

•   2.  3539 

6.5196 

7.688 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  57°. 


253 


Lat. 

log  A 
diff.l"=-0.06 

logB 
diff.l"=-0.19 

logC 
diff.l"=+0.46 

logD 
diff.l"=-0.02 

logE 
diff.l"=+0.08 

logF 
diff.lO'=-3.2 

o   / 

57  00 

8.508  6903 

8.  509  5673 

1.59028 

2.3539 

6.51% 

7.688 

1 

8.508  6899 

61 

056 

38 

6.  5201 

2 

95 

50 

083 

37 

06 

3 

91 

38 

111 

36 

10 

4 

87 

26 

139 

35 

15 

'  05 

83 

14 

166 

34 

20 

6 

79 

8.509  5603 

194 

33 

25 

7 

75 

8.  509  5591 

221 

32 

30 

8 

72 

79 

249 

30 

35 

9 

68 

67 

276 

29 

40 

10 

8.508  6864 

8.509  5556 

1.59304 

2.3528 

6.  5244 

11 

60 

44 

331 

27 

49 

12 

56 

32 

359 

26 

54 

13 

52 

20 

387 

25 

59 

14 

48 

8.509  5509 

414 

24 

64 

15 

44 

8.509  5497 

442 

22 

69 

16 

40 

85 

469 

21 

74 

17 

36 

73 

497 

20 

79 

18 

32 

62 

525 

19 

83 

• 

19 

28 

50 

552 

18 

88 

- 

20 

C.508  6825 

8.509  5438 

1.59580 

2.  3517 

6.5293 

7.682 

21 

21 

27 

608 

16 

6.  5298 

22 

17 

15 

635 

14 

6.  5303 

23 

13 

8.  509  5403 

663 

13 

08 

24 

09 

8.509  5392 

691 

12 

13 

25 

05 

80 

718 

11 

18 

26 

8.  508  6801 

68 

746 

10 

22 

27 

8.508  6797 

56 

774 

09 

27 

28 

93 

45 

801 

07 

32 

29 

90 

33 

829 

06 

37 

30 

8.  508  6786 

8.  509  5321 

1.59857 

•2.  3505 

f>.  5342 

31 

82 

8.509  5310 

885 

04 

47 

32 

78 

8.  509  5298 

912 

03 

52 

33 

74 

86 

940 

02 

57 

44 

70 

75 

968 

2.3500 

62 

35 

66 

63 

1.599% 

2.3499 

67 

36 

62 

51 

1.60023 

98 

72 

37 

58 

40 

051 

97 

76 

38 

54 

28 

079 

% 

81 

39 

51 

16 

107 

95 

86 

10 

8.  508  6747 

8.  509  5205 

1.60134 

2.  3493 

6.  5391 

7.675 

41 

43 

8.509  5193 

162 

92 

6.  5396 

42 

39 

81 

190 

91 

6.5401 

43 

35 

70 

218 

90 

06 

44 

31 

58 

246 

89 

11 

45 

27 

46 

274 

87 

16 

46 

23 

35 

301 

86 

21 

47 

20 

23 

329 

85 

26 

48 

16 

12 

357 

84 

31 

49 

12 

8.  509  5100 

385 

83 

36 

50 

8.  508  6708 

8.  509  5088 

1.60413 

2.  3481 

6.  5441 

51 

04 

77 

441 

80 

46 

52 

8.  508  6700 

65 

469 

79 

50 

53 

8.508  6696 

54 

4% 

78 

55 

54 

92 

42 

524 

76 

60 

55 

89 

30 

552 

75 

65 

56 

85 

19 

580 

74 

70 

57 

81 

8.509  5007 

608 

73 

75 

58 

77 

8.509  49% 

636 

72 

80 

M 

73 

84 

664 

70 

85 

60 

8.5086669 

8.509  4972 

1.60692 

2.  3469 

6.5490 

7.  669 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  58°. 


Lat. 

log  A 
diff.l"=-0.06 

logB 
diff.l"=-0.19 

logC 
diff.l"=+0.47 

logD 
diff.l"=-0.02 

log  E        log  F 
diff.  1"=  +0.08  diff.  10'=-3.3 

o   / 

58  00 

8.  508  6669 

8.  509  4972 

1.  60692 

2.3469 

6.  5490       '  7.  669 

1 

65 

61 

720 

68 

6.5495 

2 

62 

49 

748 

67 

6.5500 

3 

58 

38 

776 

66 

05 

4 

54 

26 

804 

64 

10 

05 

50 

14 

832 

63 

15 

6 

46 

8.  509  4903 

860 

62 

20 

7 

42 

8.  509  4891 

888 

61 

25 

8 

38 

80 

916 

59 

30 

9 

35 

68 

944 

58 

35 

10 

8.  508  6631 

8.  509  4857 

1.60972 

2.3457 

6.5540 

11 

27 

45 

1.61000 

56 

45 

12 

23 

33 

028 

54 

50 

13 

19 

22 

056 

53 

55 

14 

15 

8.  509  4810 

084 

52 

60 

15 

11 

8.  509  4799 

112 

51 

65 

16 

08 

87 

140 

49 

70 

17 

04 

76 

168 

48 

75 

18 

8.  508  6600 

64 

197 

47 

80 

19. 

8.  508  6596 

53 

225 

46 

85 

20 

8.508  6592 

8.  509  4741 

1.61253 

2.3444 

6.5590         7.362 

21 

88 

30 

281 

43 

6.5595 

22 

85 

18 

309 

42 

6.5600 

23 

81 

8.  509  4707 

337 

41- 

05 

24 

77 

8.  509  4695 

365 

39 

10 

25 

73 

84 

393 

38 

15 

26 

69 

72 

422 

37 

20 

27 

65 

61 

450 

35 

25 

28 

62 

49 

478 

34 

30 

29 

58 

38 

506 

33 

35 

30 

8.508  6554 

8.  509  4626 

1.61534 

2.  3432 

6.5640 

31 

50 

15 

563 

30 

45 

32 

46 

8.  509  4603 

591 

29 

50 

33 

42 

8.509  4592 

619 

28 

55 

34 

39 

80 

647 

26 

60 

35 

35 

69 

675 

25 

65 

36 

31 

57 

704 

24 

70 

37 

27 

46 

732 

23 

75 

38 

23 

35 

760 

21 

80 

39 

20 

23 

789 

20 

86 

40 

8.  508  6516 

8.509  4512 

1.61817 

2.  3419 

6.5691         7.656 

41 

12 

8.509  4500 

845 

17 

6.5696 

42 

08 

8.  509  4489 

873 

16 

6.  5701 

43 

04 

77 

902 

15 

06 

44 

8.508  6500 

66 

930 

14 

11 

45 

8.  508  6497 

54 

958 

12 

16 

46 

93 

43 

1  .  61987 

11 

21 

47 

89 

32 

1.62015 

10 

26 

48 

85 

20 

043 

08 

31 

49 

81 

8.  509  4409 

072 

07 

36 

50 

8.  508  6478 

8.509  4397 

1.62100 

2.3406 

6.  5741 

51 

74 

86 

129 

04 

46 

52 

70 

74 

157 

03 

51 

53 

66 

63 

185 

02 

56 

54 

62 

52 

214 

2.3400 

62 

55 

59 

40 

242 

2.  3399 

67 

56 

55 

29 

271 

98 

72 

57 

51 

17 

299 

96 

77 

58 

47 

8.  509  4306 

327 

95 

82 

59 

43 

8.  509  4295 

356 

94 

87 

60 

8.508  6440 

8.  509  4283 

1.62384 

2.3392 

6.  5792        7.  649 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computation!) — Continued. 
LATITUDE  59°. 


255 


Lat. 

log  A 
diff.l"=-0.06 

logB 
diff.l"=.-0.19 

logC 
diff.l"=+0.48 

logD 
diff.l"=-0.02 

logE 
diff.l"=  +0.09 

losrF 

diff.lO'  =  -3.5 

o   / 

59  00 

8.  508  6440 

8.509  4283 

1.62384 

2.3392 

6.  5792 

7.649 

1 

36 

72 

413 

91 

6.  5^97 

2 

32 

61 

441 

90 

6.5802 

3 

28 

49 

470 

88 

07 

4 

24 

38 

498 

87 

13 

5 

21 

26 

527 

86 

18 

6 

17 

15 

555 

84 

23 

7 

13 

8.  509  4204 

584 

83 

28 

8 

09 

8.  509  4192 

612 

82 

33 

9 

05 

81 

641 

80 

38 

10 

8.  508  6402 

8.509  4170 

1.62669 

2.  3379 

6.  5843 

11 

8.  508  6398 

58 

698 

78 

48 

12 

94 

47 

727 

76 

54 

13 

90 

36 

755 

75 

59 

14 

87 

24 

784 

74 

64 

15 

83 

13 

812 

72 

69 

16 

79 

8.  509  4102 

841 

71 

.  74 

17 

75 

8.509  4090 

870 

69 

79 

18 

71 

79 

898 

68 

84 

19 

68 

68 

927 

67 

89 

20    8.  508  6364 

8.509  4056 

1.62955 

2.  3365 

6.  5895 

7.642 

21 

60 

45 

1.62984 

64 

6.5900 

22 

56 

34 

1.63013 

63 

05 

23 

53 

22 

041 

61 

10 

24 

49 

11 

070 

60 

15 

25 

45 

8.509  4000 

099 

58 

20 

26 

41 

8.  509  3989 

127 

57 

26 

27 

38 

77 

156 

56 

31 

28 

34 

66 

185 

54 

36 

29 

30 

55 

214 

53 

41 

30 

8.  508  6326 

8.  509  3943 

1.63242 

2.3351 

6.  5946 

31 

23 

32 

271 

50 

51 

32 

19 

21 

300 

49 

57 

33 

15 

8.509  3910 

329 

47 

62 

34 

11 

8.  509  3898 

357 

46 

67 

35 

08 

87 

386 

44 

72 

36 

04 

76 

415 

43 

77 

37 

8.  508  6300 

65 

444 

42 

82 

38 

8.  508  62% 

53 

473 

40 

88 

39 

93 

42 

501 

39 

.93 

40 

8.  508  6289 

8.  509  3831 

1.63530 

2.3337 

6.5998 

7.635 

41 

85 

20 

559 

36 

6.6003 

42 

81 

8.509  3808 

588 

35 

08 

43 

78 

8.509  3797 

617 

33 

14 

44 

74 

86 

646 

32 

19 

45 

70 

75 

674 

30 

24 

46 

66 

63 

703 

29 

29 

47 

63 

52 

732 

28 

34 

48 

59 

41 

761 

26 

40 

49 

55 

30 

790 

25 

45 

50 

8.  508  6251 

8.509  3719 

1.03819 

2.  3323 

6.6050 

51 

48 

8.  509  3708 

848 

22 

55 

52 

44 

8.  509  3696 

877 

20 

61 

53 

40 

85 

906 

19 

66 

54 

36 

74 

935 

17 

71 

55 

33 

63 

964 

16 

76 

56 

29 

52 

1.63993 

15 

81 

57 

25 

40 

1.64022 

13 

87 

58 

22 

29 

051 

12 

92 

59 

18 

18 

080 

10 

G.  6097 

60 

8.  508  6214 

8.  50V  4607 

1.64109 

2.3309 

6.  6102 

7.627 

256 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — -Geodetic  position  computations — Continued. 

LATITUDE  60°. 


Lat, 

log  A 
diff.  1"=-0.06 

logE 
diff.  1"=-0. 

logC 
iC  diff.  1"=+0.49 

logD 
diff.  1"=-0.0 

log  E       log  F 
3  diff.  1"=  +0.09  diff.lO'=  -3.7 

O     1 

CO  00 

8.  508  6214 

8.  509  3607 

1.64109 

2.3309 

6.  6102       7.  627 

1 

10 

8.509  3596 

138 

07 

08 

2 

07 

85 

167 

06 

13 

3 

8.508  6203 

73 

196 

04 

18 

x   4 

8.  508  6199 

62 

225 

03 

23 

05 

96 

51 

254 

02 

29 

6 

92 

40 

283 

2.3300 

34 

7 

88 

29 

312 

2.3299 

39 

8 

84 

18 

"841 

97 

44 

9 

81 

8.509  3507 

370 

96 

50 

10 

8.  508  6177 

8.509  3495 

1.  64400 

2.  3294 

6.6155 

11 

73 

84 

429 

93 

60 

12 

70 

73 

458 

91 

66 

13 

66 

62 

487 

90 

71 

14 

62 

51 

516 

88 

76 

15 

58 

40 

545 

87 

81 

16 

55 

29 

574 

85 

87 

17 

51 

18 

604 

84 

92 

18 

47 

8.  509  3407 

633 

82 

6.  6197 

13 

44 

8.  509  3395 

662 

81 

6.  6203 

20 

8.  508  6140 

8.509  3384 

1.64691 

2.  3279 

6.6208       7.620 

21 

36 

73 

720 

78 

13 

22 

33 

62 

750 

76 

18 

23 

29 

51 

779 

75 

24 

24 

25 

40 

808 

73 

29 

25 

21 

29 

838 

72 

34 

26 

18 

18 

867 

70 

40 

27 

14 

8.  509  3307 

896 

69 

45 

28 

10 

8.  509  32% 

925 

67 

50 

29 

07 

85 

955 

66 

56 

30    8.  508  6103 

8.509  3274 

1.64984 

2.  3264 

6.  6261 

31    8.  508  6099 

63 

1.65013 

63 

66 

32 

% 

52 

043 

61 

72 

33 

92 

40 

072 

60 

77 

34 

88 

29 

101 

58 

82 

35 

85 

18 

131 

57 

87 

36 

81 

8.  509  3207 

160 

55 

93 

37 

77 

8.  509  3196 

190 

54 

6.  6298 

38 

74 

85 

219 

52 

6.  6304 

39 

70 

74 

248 

51 

09 

40 

8.508  6066 

8.  509  3163 

1.65278 

2.3249 

6.6314       7.613 

41 

63 

52 

307 

48 

20 

42 

59 

41 

337 

46 

25 

43 

55 

30 

366 

45 

30 

44 

52 

19 

3% 

43 

36 

45 

48 

8.  509  3108 

425 

41 

41 

46 

44 

8.509  3097 

455 

40 

46 

47 

41 

86 

484 

38 

52 

48 

37 

75 

514 

37 

57 

49 

33 

64 

543 

35 

62 

50 

8.  508  6030 

8.509  3053 

1.65573 

2.  3234 

6.6368 

51 

26 

42 

602 

32 

73 

52 

22 

31 

632 

31 

79 

53 

19 

20 

661 

29 

84 

54 

15 

8.509  3010 

691 

28 

89 

55 

11 

8.509  2999 

721 

26 

6.6395 

56 

08 

88 

750 

24 

6.6400 

57 

04 

77 

780 

23 

05 

58 

8.  508  6000 

66 

809 

21 

11 

59 

8.  508  5997  . 

55 

839 

20 

16 

60 

•  8.  508  5993 

8.509  2944 

1.65869 

2.  3218 

C.  6422     .  7.  605 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued, 
LATITUDE  61°. 


257 


Lat. 

log  A 
diff.l"=-0.06 

logB 
diff.l"=-0.18 

logC 
diff.l"=+0.50 

logD 
diff.l"=-0.03 

logE 
diff.l"=+0.09 

logF 
diff.lO'=-4.0 

o   / 
61  00 

8.  508  5993 

8.509  2944 

1.65869 

2.3218 

6.6422 

7.605 

1 

89 

33 

898 

17 

27 

2 

86 

22 

928 

15 

32 

3 

82 

11 

958 

13 

38 

4 

79 

5.509  2900 

1.  65987 

12 

43 

05 

75 

8.509  2889 

1.66017 

10 

48 

6 

71 

78 

047 

09 

54 

7 

68 

67 

076 

07 

59 

8 

64 

56 

106 

06 

65 

9 

60 

46 

136 

04 

70 

10 

8.  508  5957 

8.  509  2835 

1.66166 

2.3202 

6.  6476 

11 

53 

24 

195 

2.  3201 

81 

12 

49 

13 

225 

2.  3199 

87 

13 

46 

8.  509  2802 

255 

98 

92 

14 

42 

8.  509  2791 

285 

% 

6.  6497 

15 

39 

80 

315 

94 

6.  6503 

16 

35 

69 

344 

93 

08 

17 

31 

58 

374 

91 

14 

18 

28 

48 

404 

90 

19 

19 

24 

37 

434 

88 

25 

20     8.  508  5920 

8.509  2726 

1.66464 

.   2.  3186 

6.  6530 

7.597 

21          17 

15 

494 

85 

36 

22 

13 

8.509  2704 

524 

83 

41 

23 

10 

8.  509  2693 

553 

81 

46 

24          06 

83 

583 

80 

52 

25 

8.508  5902 

72 

613 

78 

57 

26 

8.508  5899 

61 

643 

77 

63 

27 

95 

50 

673 

75 

68 

28 

92 

39 

703 

73 

74 

29 

88 

28 

733 

72 

79 

30 

8.508  5884 

8.  509  2618 

1.66763 

2.  3170 

6.  6585 

31 

81 

8.  509  2607 

793 

68 

90 

32 

77 

8.  509  2696 

823 

67 

6.  6596 

33 

74 

85 

853 

65 

6.  6601 

34 

70 

74 

883 

64 

07 

35 

66 

64 

913 

S2 

12 

36 

63 

53 

943 

60 

18 

37 

59 

42 

1.66973 

58 

23 

38 

56 

31 

1.67003 

57 

29 

39 

52 

20 

033 

55 

34 

40 

8.508  5848 

8.  509  2510 

1.67063 

2.  3154 

6.  6640 

7.589 

41 

45 

8.  509  2499 

094 

52 

45 

42 

41 

88 

124 

50 

51 

43 

38 

77 

154 

49 

|6 

44 

34 

67 

184 

47 

62 

45 

30 

56 

214 

45 

67 

46 

27 

45 

244 

44 

73 

47 

23 

34 

274 

42 

78 

48 

20 

24 

305 

40 

84 

49 

16 

1° 

335 

39 

89 

50 

8.  508  5813 

8.  509  2402 

1.  67365 

2.  3137 

6.  6695 

51 

09 

8.  509  2391 

395 

35 

6.6700 

52 

05 

81 

425 

34 

06 

53 

8.508  5802 

70 

456 

32 

12 

54 

8.  508  5798 

59 

486 

30 

17 

55 

95 

49 

516 

29 

23 

56 

91 

38 

547 

27 

28 

57 

88 

27 

577 

25 

34 

'58 

84 

16 

607 

23 

39 

59 

80 

8.  509  2306 

637 

22 

45 

60 

8.508  5777 

8.5092295 

1.07668 

2.  3120 

6.6750 

7.  581 

46061—08 17 


258 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23.  —  Geodetic  position  computations — Continued. 
LATITUDE  62°. 


Lat. 

log  A 
diff.l"=-0.06 

logB 
diff.  1"=  -0.18 

logC 
d  iff.  1"=  +0.51 

logD 
diff.l"=-0.03 

logE 
diff.  1"=  +0.09 

logF 
diff.  10'  =  -4.2 

o   /  ' 

• 

62  00 

8.  508  5777 

8.  509  2295 

1.  67668 

2.  3120 

6.6750 

7.581 

1 

73 

84 

698 

18 

56 

2 

70 

74 

728 

17 

61 

3 

66 

63 

759 

15 

67 

4 

63 

52 

789 

13 

73 

05 

59 

42 

820 

12 

78 

6 

55 

31 

850 

10 

84 

7 

52 

20 

880 

08 

89 

8 

48 

8.  509  2210 

911 

06 

6.  6795 

9 

45 

8.509  2199 

941 

05 

6.6801 

10 

8.  508  5741 

8.  509  2188 

1.67972 

2.3103 

6.6806 

11 

38 

78 

1.68002 

01 

12 

12 

34 

67 

033 

2.3100 

17 

13 

30 

56 

063 

2.3098 

23 

14 

27 

46 

094 

96 

29 

15 

24 

35 

124 

94 

34 

16 

20 

25 

155 

93 

40 

17 

16 

14 

185 

91 

45 

18 

13 

8.509  2103 

216 

89 

51 

19 

09 

8.  509  2093 

246 

87 

57 

20 

8.508  5706 

8.  509  2082 

1.68277 

2.  3086 

6.  6»62 

7.573 

21 

8.  508  5702 

71 

307 

84 

68 

22 

8.  508  5699 

61 

338 

82 

73 

23 

95 

50 

369 

80 

79 

24 

92 

40 

399 

79 

85 

25 

88 

29 

430 

77 

90 

26 

85 

19 

461 

75 

6.6896 

27 

81 

8.  509  2008 

491 

74 

6.6902 

28 

78 

8.  509  1997 

522 

72 

07 

29 

74 

87 

553 

-  70 

13 

30 

8.  508  5671 

8.509  1976 

1,68583 

2.3068 

6.  6919 

31 

67 

66 

614 

66 

24 

32 

64 

55 

645 

65 

30 

33 

60 

45 

675 

63 

36 

34 

56 

34 

706 

61 

41 

35 

53 

23 

737 

59 

47 

36 

49 

13 

768 

58 

53 

37 

46 

8.509  1902 

799 

56 

58 

38 

42 

8.509  1892 

829 

54 

64 

39 

39 

81 

860 

52 

70 

40 

8.  508  5635 

8.509  1871 

1.68891 

2.3050 

6.  6975 

7.564 

41 

32 

60 

922 

49 

81 

42 

28 

50 

953 

47 

87 

43 

25 

39 

1.68984 

45 

92 

44 

21 

29 

1.  69014 

43 

6.  6998 

45 

18 

18 

045 

42 

6.7004 

46 

14 

8.509  1808 

076 

40 

09 

47 

11 

8.  509  1797 

107 

38 

15 

48 

07 

87 

138 

36 

21 

49 

04 

76 

169 

34 

26 

50 

8.  508  5600 

8.509  1766 

1.69200 

2.  3033 

6.  7032 

51 

8.  508  5597 

55 

231 

31 

38 

52 

93 

45 

262 

29 

44 

53 

90 

34 

293 

27 

49 

54 

86 

24 

324 

25 

55 

55 

83 

14 

355 

23 

61 

56 

80 

8.509  1703 

386 

22 

67 

57 

76 

8.509  1693 

417 

-20 

72 

58 

73 

82 

448 

18 

78 

59 

69 

72 

479 

16 

84 

60 

8.  508  5566 

8.509  1661 

1.69510 

2.3014 

6.  7089 

7.556 

GEOGRAPHIC    TABLES    AND   FORMULAS. 

TAHLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  63°. 


259 


Lat. 

log  A 
diff.l"=-0.06 

logB 
diff.l"=-0.17 

logC 
diff.l"=+0.52 

logD 
diff.l"=-0.03 

logE 
diff.l"=+0.10  d 

logF 
iff.  10'  =  -4.5 

o   / 

63  00 

8.508  ;Vx;r> 

8.  509  1661 

1.69510 

2.  3014 

6.  7089 

7.556 

1 

62 

51 

541 

13 

6.  7095 

2 

59 

40 

572 

11 

6.  7101 

3 

55 

30 

603 

09 

07 

4 

52 

20 

635 

07 

12 

05 

48 

8.  509  1609 

666 

05 

18 

6 

45 

8.  509  1599 

697 

03 

24 

7 

41 

88 

728 

02 

30 

8 

38 

78 

759 

2.3000 

35 

9 

34 

68- 

791 

2.  2998 

41 

10 

8.508  5531 

8.509  1557 

1.69822 

2.  2996 

6.  7147 

11 

27 

47 

853 

94 

53 

12 

24 

36 

884 

92 

59 

13 

20 

26 

915 

90 

64 

14 

17 

16 

947 

89 

70 

15 

14 

8.509  1505 

1.69978 

87 

76 

16 

10 

8.509  1495 

1.70009 

85 

82 

17 

07 

85 

041 

83 

88 

18 

03 

74 

072 

81 

93 

19 

8.508  5500 

64 

103 

79 

6.7199 

20 

8.  508  5496 

8.  509  1454 

1.70135 

2.2977 

6.  7205 

7.547 

21 

93 

43 

166 

75 

11 

22 

89 

33 

197 

74 

17 

23 

86 

23 

229 

72 

22 

24 

83 

12 

260 

70 

28 

25 

79 

8.509  1402 

292 

68 

34 

26 

76 

8.509  1392 

323 

66 

40 

27 

72 

81 

355 

64 

46 

28 

69 

71 

386 

62 

51 

29 

65 

61 

417 

60 

57 

30 

8.  508  5462 

8.  509  1350 

1.70449 

2.2958 

6.  7263 

31 

5* 

40 

480 

57 

69 

32 

55 

30 

512 

55 

75 

33 

52 

19 

544 

53 

81 

34 

48 

8.509  1309 

575 

51 

86 

35 

45 

*.  509  1299 

607 

49 

92 

36 

41 

89 

638 

47 

6.  7298 

37 

38 

78 

670 

45 

6.  7304 

38 

34 

68 

701 

43 

10 

39 

31 

58 

733 

41 

16 

40 

8.508  5428 

8.  509  1248 

1.70765 

2.  2939 

6.  7322 

7.  538 

41 

24 

37 

796 

37 

28 

42 

21 

27 

828 

36 

33 

43 

17 

17 

860 

.34 

39 

44 

14 

8.509  1207 

891 

32 

45 

45 

11 

8.509  1196 

923 

30 

51 

46 

07 

86 

955 

28 

57 

47 

04 

76 

1.70986 

26 

63 

48 

8.  508  5400 

66 

1.71018 

24 

69 

49 

8.  508  5397 

55 

050 

22 

75 

50 

8.  508  5394 

8.509  1145 

1.  71082 

2.  2920 

6.7381 

51 

90 

35 

114 

18 

86 

52 

87 

25 

145 

16 

92 

53 

83 

15 

177 

14 

6.  7398 

54. 

80 

8.509  1104 

209 

12 

6.7404 

55 

77 

8.  ,509  1094 

241 

10 

10 

56 

73 

84 

273 

08 

16 

57 

70 

74 

305 

06   - 

22 

58 

66 

64 

337 

04 

28 

59 

n 

54 

368 

02 

34 

60 

8.  508  5360 

8.509  1043 

1.71400 

2.2901 

6.  7440 

7.529 

260 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  64°. 


Lat. 

log  A 
diff.  1"=-0.06 

logB 
diff.  l"=  -0.17 

log  C 
diff.  1"=  +0.54 

logD 
diff.  1"=  -0.03  diff. 

log  E 

1"=+0.10  diff. 

log  F 

10'  =  -4.7 

0    / 

64  00 

8.  508  5360 

8.509  1043 

1.71400 

2.  2901 

6.  7440 

7.  529 

1 

56 

33 

432 

2.  2899 

46 

2 

53 

23 

464 

-   97 

52 

'3 

49 

13 

496 

95 

58 

4 

46 

8.509  1003 

528 

93 

63 

05 

43 

8.  509  0993 

560 

91 

69 

6 

39 

82 

592 

89 

75 

7 

36 

72 

624 

87 

81 

8 

33 

62 

656 

85 

87 

9 

29 

52 

•688 

83 

93 

10 

8.  508  5326 

8.509  0942 

1.71720 

2.  2881 

6.  7499 

11 

22 

32 

752 

79 

6.  7505 

12 

19 

22 

785 

77 

11 

13 

16 

12 

817 

75 

17 

14 

12 

8.509  0902 

849 

73 

23 

15 

09 

8.  509  0891 

881 

71 

29 

16 

06 

81 

913 

69 

35 

17 

8.508  5302 

71 

945 

67 

41 

18 

8.  508  5299 

61 

1.71977 

65 

47 

19 

96 

51 

1.  72010 

63 

53 

20 

8.  508  5292 

8.  509  0841 

1.  72042 

'2.  2861 

6.  7559 

7.  520 

21 

89 

31 

074 

59 

65 

22 

85 

21 

106 

57 

71 

28 

82 

11 

139 

55 

77 

24 

79 

8.509  0801 

171 

53 

83 

25 

75 

8.  509  0791 

203 

51 

89 

26 

72 

81 

235 

49 

6.  7595 

27 

69 

71 

268 

47 

6.  7601 

28 

65 

61 

300 

45 

07 

29 

62 

51 

332 

42 

13 

30 

8.  508  5259 

8.  509  0741 

1.  72365 

2.  2840 

6.  7619 

31 

55 

31 

397 

38 

25 

32 

52 

21 

430 

36 

31 

33 

49 

11 

462 

34 

37 

34 

45 

8.509  0701 

495 

32 

43 

35 

42 

8.  509  0691 

527  • 

30 

49 

36 

39 

81 

559 

28 

56 

37 

35 

71 

592 

26 

62 

38 

32 

61 

624 

24 

68 

39 

29 

51 

657 

22 

74 

40 

8.  508  5225 

8.509  0641 

1.72689 

2.  2820 

6.  7680 

7.511 

41 

22 

31 

722 

18 

86 

42 

19 

21 

755 

16 

92 

43 

15 

11 

787 

14 

6.  7698 

44 

12 

8.509  0601 

820 

12 

6.  7704 

45 

09 

8.509  0591 

852 

10 

10 

46 

05 

81 

885 

07 

16 

47 

8.  508  5202 

71 

918 

05 

22 

48 

8.  508  5199 

61. 

950 

03 

28 

49 

95 

51 

1.72983 

2.2801 

35 

50 

8.508  5192 

8.  509  0541 

1.73016 

2.  2799 

6.  7741 

51 

89 

31 

048 

97 

47 

52 

86 

21 

081 

95 

53 

53 

82 

11 

114 

93 

59 

54 

79 

8.  509  0501 

146 

91 

65 

55 

76 

8.  509  0491 

179 

89 

71 

56 

72 

82 

212 

87 

77 

57 

.  69 

72 

245 

84 

84 

58 

66 

62 

278 

82 

90 

59 

62 

52 

310 

80 

6.7796 

60 

8.5085159 

8.509  0442 

1.73343 

2.  2778 

6.  7802 

7.501 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  65°. 


261 


Lat. 

log  A 

logB 
diff.l"=-0.16 

logC 
diff.l"=+0.56 

logD 
diff.l"—  0.04 

logE 
diff.l"=+0.10 

logP 
diff.lO'  =  -5.0 

o   / 
65  00 

8.  508  5159 

8.509  0442 

1.73343 

12.  277S 

6.  7802 

7.501 

1 

56 

32 

376 

76 

08 

2 

52 

22 

409 

74 

14 

3 

49 

12 

442 

72 

20 

4 

46 

8.509  0402 

475 

70 

27 

05 

43 

8.  509  0393 

508 

68 

33 

6 

39 

83 

541 

65 

39 

7 

36 

73 

574 

63 

45 

8 

33 

63 

607 

61 

51 

9 

30 

53 

640 

59 

57 

10 

8.  508  5126 

8.5090344 

1.  73673 

2.  2757 

6.7864 

11 

23 

34 

706 

55 

70 

12 

20 

24 

739 

53 

76 

13 

17 

14 

772 

50 

82 

14 

13 

8.509  0304 

805 

48 

88 

15 

10 

8.  509  0295 

838 

46 

6.  7895 

16 

07 

85 

871 

44 

6.7901 

17 

03 

75  - 

904 

42 

07 

18 

8.  508  5100 

65 

937 

40 

13 

19 

8.  508  5097 

55 

1.  73970 

38 

19 

20 

8.508  5094 

8.509  0245 

1.74004 

2.  2735 

6.7926 

7.491 

21 

90 

36 

037 

33 

32 

22 

87 

26 

070 

31 

38 

23 

84 

16 

103 

29 

44 

24 

81 

8.5090206 

136 

27 

51 

25 

77 

8.  509  0197 

170 

24 

57 

26 

74 

87 

203 

22 

63 

27 

71 

77 

236 

20 

69 

28 

68 

67 

270 

.  18 

76 

29 

64 

57 

303 

16 

82 

30 

8.508  5061 

8.5090148 

1.  74336 

2.  2714 

6.  7988 

31 

58 

38 

370 

11 

6.7994 

32 

54 

28 

403 

09 

6.8001 

33 

51 

18 

436 

07 

07 

34 

48 

8.509  0109 

470 

or> 

13 

35 

45 

8.5090099 

503 

03 

19 

36 

41 

89 

537 

2.2700 

26 

37 

38 

80 

570 

2.  2698 

32 

38 

35 

70 

604 

96 

38 

39 

32 

60 

637 

94 

44 

40 

8.508  5029 

8.  509  0051 

1.74670 

2.2692 

6.  8051 

7.481 

41 

25 

41 

704 

89 

57 

42 

22 

31 

738 

87 

63 

43 

19 

22 

771 

85 

70 

44 

16 

12 

805 

83 

76 

45 

13 

8.509  0002 

838 

80 

82 

46 

09 

'8.  508  9993 

872 

78 

89 

47 

06 

83 

906 

76 

6.8095 

48 

»        03 

73 

939 

74 

6.8101 

49 

8.5085000 

64 

1.74973 

72 

07 

50 

8.508  49% 

8.  508  9954 

1.75007 

2.  2669 

6.  8114 

51 

93 

44 

040 

67 

20 

52 

90 

35 

074 

65 

27 

63 

87 

,  25 

108 

63 

33 

54 

84 

15 

142 

60 

39 

55 

80 

8.508  9906 

175 

68 

46 

56 

77 

8.  508  98% 

209 

56 

52 

57 

74 

87 

243 

53 

58 

58 

71 

77 

277 

51 

65 

59 

t;s 

67 

311 

49 

71 

60 

8.508  4964 

8.5089858 

1.75344 

2.2647 

6.  8177 

7.471 

262 


GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  66°. 


Lat. 

log  A 
diff.l"=-0.05 

logB 
diff.l"=-0.16 

logC 
diff.l"=+0.57 

logD 
diff.l"=-0.04 

log  E        log  F 
diff.l"=+0.11  diff.  10'=-5.3 

o   / 
66  00 

8.  508  4964 

8.  508  9858 

1.75344 

2.  2647 

6.8177       7.471 

£ 

61 

48 

378 

44 

84 

2 

58 

39 

412 

42 

90 

3 

55 

29 

446 

40 

6.  8196 

4 

52 

20 

480 

38 

6.  8203 

05 

48 

10 

514 

35 

09 

6 

45 

8.  508  9801 

548 

33 

16 

7 

42 

8.  508  9791 

582 

31 

22 

8 

39 

82 

616 

28 

28 

9 

36 

72 

650 

26 

35 

10 

8.508  4933 

8.  508  9762 

1.75684 

2.  2624 

6.  8241 

11 

29 

53 

718 

22 

48 

12 

26 

43 

752 

19 

54 

13 

23 

34 

786 

17 

61 

14 

20 

24 

820 

15 

67 

15 

17 

14 

854 

12 

73 

16 

13 

8.5089705 

889 

10 

80 

17 

10 

8.  508  9696 

923 

08 

86 

18 

07 

86 

957 

05 

93 

19 

04 

77 

1.  75991 

03 

6.8299 

20 

8.  508  4901 

8.508  9667 

1.76025 

2.  2601 

6.  8306        7.  461 

21 

8.  508  4898 

58 

060 

2.  2598 

12 

22 

95 

48 

094 

96 

19 

23 

91 

39 

128 

94 

25 

24 

88 

29 

163 

91 

31 

25 

85 

20 

197 

89 

38 

26 

82 

11 

231 

87 

44 

27 

79 

8.  508  9601 

266 

84 

51 

28 

76 

8.  508  9592 

300 

82 

57 

29 

73 

82 

334 

80 

64 

30 

8.  508  4869 

8.  508  9573 

1.76369 

2.2578 

6.8370 

31 

66 

63 

403 

75 

77 

32 

63 

54 

438 

73 

83 

33 

60 

44 

472 

70 

90 

34 

57 

35 

507 

68 

6.8396 

35 

54 

25 

541 

66 

6.8403 

36 

50 

16 

576 

63 

09 

37 

47 

8.  508  9507 

610 

61 

16 

38 

44 

8.  508  9497 

645 

59 

22 

39 

41 

88 

679 

56 

29 

40 

8.  508  4838 

8.  508  9478 

1.  76714 

2.2554 

6.  8436        7.  450 

41 

35 

69 

749 

51 

42 

42 

32 

60 

783 

49 

49 

43 

29 

51 

818 

47 

55 

44 

26 

41 

853 

44 

62 

45 

22 

32 

887 

42 

68 

46 

19 

23 

922 

39 

75 

47 

16 

13 

957 

37 

81 

48 

13 

8.508  9404 

1.  76991 

35 

88 

49 

10 

8.  508  9395 

1.  77026 

32 

6.  8495 

50 

8.  508  4807 

8.508  9385 

1.  77061 

2.  2530 

6.8501 

51 

04 

76 

096 

27 

08 

52 

8.508  4801 

66 

131 

25 

14 

53 

8.  508  4797 

57 

166 

28 

21 

54 

94 

48 

200  ' 

20 

27 

55 

91 

38 

235 

18 

34 

56 

88 

29 

270 

15 

41 

57 

85 

20 

305 

13 

47 

58 

82 

10 

340 

11 

54 

59 

79 

8.  508  9301 

375 

08 

60 

60 

8.5084776 

8.608  9292 

1.  77410 

2.2506 

6.8667       7.440 

GEOGRAPHIC   TABLES    AND   FORMULAS. 
TABLE  23. — Geodetic  position  compulations — Continued. 

LATITUDE  67°. 


263 


Lat. 

log  A 
diff.l"=-0.05 

logB 
diff.l"=-0.15 

logC 
diff.l"=+OT59 

logD 
diff.l"=-0.04 

logE 
diff.l"=+0.11 

logF 
diff.lO'=-5.6 

0    / 

67  00 

8.508  4776 

8.  508  9292 

1.  77410 

2.2506 

6.8567 

7.440 

1 

73 

83 

445 

03 

74 

2 

70 

73 

480 

2.2501 

80 

3 

66 

64 

515 

2.  2498 

87 

4 

63 

55 

550 

96 

6.8594 

05 

60 

46 

585 

93 

6.8600 

6 

57 

36 

620 

91 

07 

7 

54 

27 

656 

89 

14 

8 

51 

18 

691 

86 

20 

9 

48 

8.508  9208 

726 

84 

27 

10 

8.5084745 

8.508  9199 

1.77761 

2.2481 

6.8634 

11 

42 

90 

796 

79 

40 

12 

39 

81 

831 

76 

47 

13 

36 

72 

867 

74 

54 

14 

33 

62 

902 

71 

60 

15 

30 

53 

937 

69 

67 

16 

26 

44 

1.77973 

66 

74 

17 

23 

35 

1.78008 

64 

80 

18 

20 

26 

043 

61 

87 

19 

17 

16 

079 

59 

6.8694 

20 

8.  508  4714 

8.508  9107 

1.78114 

2.2456 

6.8700 

7.429 

21 

11 

8.508  9098 

149 

64 

07 

22 

08 

89 

185 

51 

U 

23 

05 

80 

220 

49 

20 

24 

8.  508  4702 

71 

256 

46 

27 

25 

8.  508  4699 

62 

291 

44 

34 

26 

96 

52 

327 

41 

41 

27 

93 

43 

362 

39 

47 

28 

90 

34 

398 

36 

54 

29 

87 

25 

433 

34 

61 

30 

8.508  4684 

•  8.  508  9016 

1.78469 

2.2431 

6.8768 

31 

81 

8.508  9007 

505 

29 

74 

32 

78 

8.  608  8998 

540 

26 

81 

33 

75 

88 

576 

24 

88 

34 

72 

79 

612 

21 

6.8795 

35 

68 

70 

647 

19 

6.8802 

36 

65 

61 

683 

16 

08 

37 

62 

52 

719 

14 

15 

38 

59 

43 

756 

11 

22 

39 

56 

34 

790 

09 

29 

* 

40 

8.5084653 

8.508  8925 

1.78826 

2.?406 

6.8835 

7.418 

41 

50 

16 

862 

J3 

42 

42 

47 

8.  508  8907 

898 

2.2401 

49 

43 

44 

8.  508  8898 

934 

2.  2398 

56 

44 

41 

89 

1.  78970 

96 

63 

• 

45 

38 

80 

1.79006 

93 

70 

46 

35 

71 

042 

91 

76 

47 

32 

62 

078 

88 

83 

48 

29 

53 

114 

86 

90 

49 

26 

44 

150 

'   83 

6.  8897 

50 

8.508  4623 

8.508  8834 

1.79186 

2.2380 

6.8904 

51 

20 

25 

222 

78 

10 

52 

17 

16 

258 

75 

17 

53 

14 

8.508  8807 

294 

73 

24 

54 

11 

8.  508  8798 

330 

70 

31 

55 

08 

89 

366 

67 

38 

56 

05 

80 

402 

65 

45 

57 

8.508  4602 

71 

438 

62 

52 

58 

8.508  4599 

62 

474 

60 

59 

59 

96 

54 

511 

57 

65 

60 

8.508  4593 

8.  508  8746 

1.79547 

2.2354 

6.  8972 

7.406 

264 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  68°. 


Lat. 

log  A 
diff.l"=-0.05 

logB 
diff.l"  =  -0.15 

logC 
diff.l"=+0.62 

logD 
difi.l"=-0.4 

log  E        log  F 
diff.l"=+0.12  diff.lO'=.--5.9 

0    1 

68  00 

8.  508  4593 

8.  508  8745 

1.  79547 

2.2354 

6.  8972        7.  406 

1 

90 

36 

583 

52 

79 

2 

87 

27 

620 

49 

86 

3 

84 

18 

656 

47 

6.  8993 

4 

81 

09 

692 

44 

6.9000 

05 

78 

8.508  8700 

728 

41 

07 

6 

76 

8.  508  8691 

765 

39 

14 

7 

73 

82 

801 

36 

21 

8 

70 

73 

838 

33 

28 

9 

67 

64 

874 

31 

35 

10 

8.  508  4564 

8.  508  8656 

1.  79911 

2.2328 

6.9042 

11 

61 

47 

947 

26 

48 

12 

58 

38 

1.  79984 

23 

55 

13 

55 

29 

1.80020 

20 

62 

14 

52 

20 

057 

18 

69 

15 

49 

11 

093 

15 

76 

16 

46 

8.  508  8602 

130 

12 

83 

17 

43 

8.  508  8593 

166 

10 

90 

18 

40 

84 

203 

07 

6.9097 

19 

37 

75 

240 

04 

6.  9104 

20 

8.  508  4534 

8.508  8566 

1.80276 

2.2302 

6.  9111        7.  395 

21 

31 

58 

313 

2.2299 

18 

22 

28 

49 

350 

96 

25 

23 

25 

40 

387 

94 

32 

24 

22 

31 

423 

91 

39 

25 

19 

22 

460 

88 

46 

26 

16 

13 

497 

86 

53 

27 

13 

8.508  8505 

534 

83 

60 

28 

10 

8.508  8496 

571 

80 

67 

29 

07 

87 

608 

77 

74 

30 

8.  508  4504 

8.  508  8478 

1.80645 

2.2275 

6.  9181 

31 

8.  508  4501 

69 

682 

72 

88 

32 

8.  508  4499 

60 

719 

69 

6.  9195 

33 

96 

52 

756 

67 

6.9203 

34 

93 

43 

793 

64 

10 

35 

90 

34 

830 

61 

17 

36 

87 

25 

867 

58 

24 

37 

84 

17 

904 

56 

31 

38 

81 

8.508  8408 

941 

53 

38 

39 

78 

8.  508  8399 

1.  80978 

50 

45 

7.383 

40 

8.  508  4475 

8.  508  8390 

1.81015 

2.2248 

6.9252 

41 

72 

82 

052 

45 

59 

42 

70 

73 

089 

42 

66 

43 

67 

64 

127 

39 

73 

44 

64 

56 

164 

36 

80 

45 

61 

47 

201 

34 

88 

46 

58 

38 

239 

31 

6.  9295 

47 

55 

30 

276 

28 

6.9302 

48 

52 

21 

313 

26 

09 

49 

49 

12 

350 

23 

16 

50 

8.  508  4446 

8.  508  8303 

1.81388 

2.2220 

6.9323 

51 

43 

8.  508  8295 

425 

17 

30 

52 

40 

86 

463 

14 

37 

53 

38 

77 

500 

12 

45 

54 

35 

68 

538 

09 

52 

55 

32 

60 

575 

06 

69 

56 

29 

51 

613 

03 

66 

57 

26 

43 

650 

2.2201 

73 

58 

23 

34 

688 

2.  2198 

80 

59 

20 

25 

726 

95 

88 

60 

8.  508  4417 

8.  508  8217 

1.81763 

2.  2192 

6.9395        7.371 

GEOGRAPHIC    TABLES    AND    FORMULAS. 
TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  69°. 


265 


Lat. 

log  A 
diff.  1"=-0.05 

log  B 
diff.  1"=-0.14 

logC 
diff.  1"=  +0.64 

log  D 
diff.  1"=  -0.05 

logE 
diff.  1"=  +0.12 

log  F 
diff.  10'  =-6.2 

0    / 

69  00 

8.  508  4417 

8.  508  8217 

1.81763 

2.2192 

6.  9395 

7.371 

.1 

14 

08 

801 

89 

6.9402 

2 

12 

8.508  8200 

838 

87 

09 

3 

09 

8.  508  8191 

876 

84 

16 

4 

06 

82 

914 

81 

.  24 

05 

03 

74 

952 

78 

31 

6 

8.  508  4400 

65 

1.81989 

75 

38 

7 

8.  508  4397 

57 

1.82027 

72 

45 

8 

94 

48 

065 

70 

52 

9 

92 

39 

103 

67 

60 

10 

8.508  4389 

8.  508  8131 

1.  82141 

2.2164 

6.  9467 

11 

86 

22 

179 

61 

74 

12 

83 

14 

217 

58 

82 

13 

80 

8.  508  8105 

255 

55 

89 

14 

77 

8.508  8096 

293 

53 

6.9496 

15 

74 

88 

330 

50 

6.9503 

16 

71 

79 

369 

47 

11 

17 

69 

71 

407 

44 

18 

18 

66 

62 

445 

41 

25 

19 

63 

54 

483 

38 

32 

20 

8.508  436J3 

8.508  8045 

1.82521 

2.  2136 

6.9540 

7.358 

21 

57 

37 

559 

33 

47 

22 

55 

28 

597 

3D 

54 

23 

52 

20 

636 

27 

62 

24 

49 

11 

674 

24 

69 

25 

46 

8.5088003 

712 

21 

76 

26 

43 

8.508  7994 

750 

18 

84 

'  27 

40 

86 

789 

15 

91 

28 

37 

77 

827 

12 

6.  9598 

29 

35 

69 

865 

10 

6.9606 

30 

8.5084332 

8.508  7960 

1.82904 

2.  2107 

6.  9613 

31 

29 

52 

942 

04 

20 

32 

26 

43 

1.82981 

2.  2101 

28 

33 

23 

35 

1.83019 

2.  2098 

35 

34 

21 

26 

058 

95 

42 

35 

18 

18 

096 

92 

50 

36 

15 

09 

135 

89 

57 

37 

12 

8.508  7901 

173 

86 

65 

38 

09 

8.  508  7893 

212 

83 

72 

39 

06 

84 

250 

80 

79 

40 

8.  508  4304 

X.  508  7876 

1.83289 

2.2078 

6.9687 

7.346 

41 

8.  508  4301 

67 

328 

75 

6.  9694 

42 

8.508  4298 

59 

366 

72 

6.9702 

43 

95 

51 

405 

69 

09 

44 

93 

42 

444 

66 

16 

45 

90 

34 

483 

63 

24 

46  f 

87 

26 

521 

60 

31 

47 

84 

17 

560 

57 

39 

48 

81 

09 

599 

54 

46 

49 

79 

8.  508  7801 

638 

51 

54 

50 

8.508  4276 

8.508  7792 

1.83677 

2.2048 

6.9761 

51 

73 

84 

716 

45 

69 

52 

70 

75 

755 

42 

76 

53 

67 

67 

794 

39 

84 

54 

65 

59 

833 

36 

91 

55 

62 

50 

872 

33 

6.  9799 

56 

59 

-  42 

911 

30 

6.  9806 

57 

M 

34 

950 

27 

14 

58 

54 

25 

1.  83989 

24 

21 

59 

51 

17 

1.84028 

21 

29 

00 

8.  508  4248 

8.508  7709 

1.84068 

2.2018 

6.9836 

7.333 

266 


GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 

LATITUDE  70°. 


Lat. 

log  A 
diff.  1"=  -0.04 

logB 
diff.  1"=-0.14 

logC 
diff.  1"=  +0.67 

logD 
diff.  1"=  -0.05 

logE 
diff.  1"=  +0.13 

logF 
diff.lO'=-6.7 

o   / 
70  00 

8.  508  4248 

8.  508  7709 

1.84068 

2.  2018 

6.  9836 

7.333 

1 

45 

8.508  7701 

107 

15 

44 

2 

43 

8.508  7692 

146 

12 

51 

3 

40 

84 

185 

09 

59 

4 

37 

76 

225 

06 

66 

05 

34 

68 

264 

03 

74 

6 

32 

59 

303 

2.2000- 

81 

7 

29 

51 

343 

2.  1997 

89 

8 

26 

43 

382 

94 

6.  9896 

9 

23 

35 

421 

91 

6.9904 

10 

8.  508  4221 

8.508  7626 

1.  84461 

2.1988 

6.  9912 

11 

18 

18 

500 

85 

19 

12 

15 

10 

540 

82 

27 

13 

12 

8.508  7602 

579 

79 

34 

14 

10 

8.  508  7594 

619 

76 

42 

15 

07 

86 

658 

73 

50 

16 

04 

78 

698 

70 

57 

17 

8.  508  4201 

69 

738 

66 

65 

18 

8.  508  4199 

61 

778 

63 

73 

19 

96 

52 

817 

60 

80 

20 

8.  508  4193 

8.  508  7544 

1.84857 

.   2.  1957 

6.9988 

7.320 

21 

90 

36 

897 

54 

6.  9995 

22 

88 

'   28 

937 

51 

7.0003 

23 

85 

20 

1.84976 

48 

11 

24 

82 

12 

1.85016 

45 

18 

25 

80 

8.  508  7504 

056 

42 

26 

26 

77 

8.508  7495 

096 

39 

34 

27 

74 

87 

136 

36 

41 

28 

71 

79 

176 

33 

49 

29 

69 

71 

216 

29 

57 

30 

8.  508  4166 

8.508  7462 

1.85256 

2.  1926 

7.0064 

31 

63 

54 

296 

23 

72 

32 

60 

46 

336 

20 

80 

33 

58 

38 

376 

17 

88 

34 

,55 

80 

416 

14 

7.0095 

35 

52 

22 

456 

11 

7.  0103 

36 

50 

14 

497 

08 

11 

37 

47 

8.508  7406 

537 

04 

19 

38 

44 

8.  508  7398 

577 

2.1901 

26 

39 

42 

90 

618 

2.  1898 

.  34 

40 

8.  508  4139 

8.  508  7382 

1.85658 

2.  1895 

7.  0142 

7.307 

41 

36 

74 

698 

92 

50 

42 

34 

66 

739 

89 

57 

43 

31 

58 

779 

85 

65 

44 

28 

50 

819 

82 

73 

45 

26 

42 

860 

79 

81 

46 

23 

34 

900 

76 

88 

47 

20 

26 

941 

73 

7.  0196 

48 

18 

18 

1.  85981 

70 

7.0204 

49 

15 

10 

1.86022 

66 

12 

50 

8.508  4112 

8.  508  7302 

1.86063 

2.1863 

7.0220 

51 

10 

8.  508  7294 

103 

60 

27 

52 

07 

8& 

144 

57 

35 

53 

04 

77 

185 

54 

43 

.  54 

8.508  4101 

69 

225 

50 

51 

55 

8.  508  4099 

61 

266 

47 

59 

56 

96 

53 

307 

44 

67 

57 

93 

45 

348 

41 

75 

58 

91 

38 

389 

38 

82 

59 

88 

30 

430 

34 

90 

60 

8.508  4086 

8.  508  7222 

1.  86470 

.  2.  1831 

7.0298 

7.293 

GEOGRAPHIC   TABLES    AND    FORMULAS. 

TABLE  23. — Geodetic  position  computations — Continued. 
LATITUDE  71°. 


267 


Lat. 

log  A 
diff.l"  =  -0.04 

logB 
diff.l"=-0.13 

logC 
diff.l"=+0.70 

logD 
diff.l"=-0.05 

logE 
diff.l"=+0.13 

logF 
diff.lO"=-7.2 

O      1. 

71  00 

8.5084086 

8.  508  7222 

1.86470 

2.1831 

7.  0298 

7.293 

1 

83 

14 

511 

28 

7.0306 

2 

80 

8.508  7206 

552 

25 

14 

3 

78 

8.  508  7198 

593 

21 

22 

4 

75 

90 

634 

18 

30 

05 

72 

82 

675 

15 

38 

6 

70 

74 

717 

12 

46 

7 

67 

66 

758 

08 

54 

8 

64 

58 

799 

05 

62 

* 

9 

62 

50 

840 

2.1802 

70 

10 

8.  508  4059 

8.  508  7142 

1.86881 

2.  1799 

7.  0378 

11 

57 

34 

923 

95 

85 

12 

54 

27 

1.  86964 

92 

7.  0393 

13 

51 

19 

1.87005 

89 

7.0401 

14 

49 

11 

046 

86 

09 

15 

46 

8.  508  7103 

088 

82 

17 

16 

43 

8.  508  7095 

129 

79 

25 

17 

41 

87 

171 

76 

33 

18 

38 

79 

212 

72 

41 

19 

36 

72 

254 

69 

49 

20 

8.  508  4033 

8.508  7064 

1.87295 

2.  1766 

7.0457 

7.279 

21 

30 

56 

337 

62 

65 

22 

28 

48 

378 

59 

73 

23 

25 

40 

420 

56 

82 

24 

23 

S3 

462 

52 

90 

25 

20 

25 

503 

49 

7.  0498 

26 

17 

17 

545 

46 

7.0506 

27  ' 

15 

09 

587 

42 

14 

28 

12 

8.508  7002 

629 

39 

22 

29 

10 

8.508  6994 

671 

36 

30 

30 

8.508  4007 

8.508  6986 

1.  87712 

2.  1732 

7.0538 

31 

05 

78 

754 

29 

46 

32 

8.508  4002 

71 

796 

26 

54 

33 

8.  508  3999 

63 

838 

22 

62 

34 

97 

55 

880 

19 

70 

35 

94 

47 

922 

16 

79 

36 

92 

40 

1.87964 

12 

87 

37 

89 

32 

1.88006 

09 

7.  0595 

38 

86 

24 

049 

06 

7.  0603 

39 

84 

16 

091 

2.  1702 

11 

40 

8.508  3981 

8.508  6908 

1.88133 

2.1699 

7.0619 

7.265 

41 

79 

8.  508  6901 

175 

95 

27 

42 

76 

8.  508  6893 

217 

92 

36 

43 

74 

85 

260 

89 

44 

44 

71 

78 

302 

'  85 

52 

45 

68 

70 

344 

82 

60 

46 

66 

62 

387 

78 

68 

47 

63 

55 

429 

75 

77 

48 

61 

47 

472 

72 

85 

49 

58 

40 

514 

68 

7.0693 

50 

8.508  3956 

8.  508  6832 

1.88557 

2.  1665 

7.  0701 

51 

53 

24 

599 

61 

09 

52 

51 

17 

642 

58 

18 

53 

48 

09 

685 

54 

26 

54 

46 

8.508  6802 

727 

51 

34 

55 

43 

8.508  6794 

770 

48 

42 

56 

41 

86 

813 

44 

61 

57 

88 

79 

855 

41 

59 

58 

36 

71 

898 

37 

67 

59 

33 

64 

941 

34 

75 

60 

8.  508  3930 

8.  508  6756 

1.88984 

2.  1630 

7.0784 

7.250 

268 


GEOGRAPHIC    TABLES    AND    FORMULAS, 

Table  of  values  of  log  sec  %  {Aq>). 


A<p 

log  sec  i 

(A<p) 

A<p 

log  sec  i 

(A<p) 

A9 

log  sec  i 

(A<P) 

A<p 

log  sec  i 

(A9) 

A<p 

log  sec  £ 

(A9) 

i 

/ 

/ 

f 

t 

10 

0.000  000 

28 

0.000  004 

46 

0.000  010 

64 

0.  000  019 

82 

'  0.  000  031 

11 

1 

29 

4 

47 

10 

65 

19 

83 

32 

12 

1 

30 

4 

48 

11 

66 

20 

84 

32 

13 

1 

31 

4 

49 

11 

67 

21 

85 

33 

14 

1 

32 

5 

50 

11 

68 

21 

86 

34 

15 

1 

33 

5 

51 

12 

69 

22 

87 

35 

.  16 

1 

34 

5 

52 

12 

70 

22 

88 

36 

17 

1 

35 

6 

53 

13 

71 

23 

89 

18 

1 

36 

6 

54 

13 

72 

24 

90 

37 

19 

2 

37 

6 

55 

14 

73 

24 

91 

38 

20 

2 

38 

7 

56 

14 

74 

25 

92 

39 

21 

2 

39 

7 

57 

15 

75 

26 

93 

40 

22 

2 

40 

7 

58 

15 

76 

26 

94 

41 

23 

2 

41 

8 

59 

16 

77 

27 

95 

41 

24 

3 

42 

8 

60 

16 

78 

28 

96 

42 

25 

3 

43 

8 

61 

17 

79 

29 

97 

43 

26 

3 

44 

9 

62 

18 

80 

29 

98 

44 

27 

3 

45 

9 

63 

18 

81 

30 

99 

45 

To  convert: 

To  convert: 

Meters  to  feet. 

Feet  to  meters. 

Kilometers  to  stat- 

Statute miles  to 

ute  miles. 

kilometers. 

1 

=    3.280833 

1  = 

0.304  8006 

1  =  0.  621  3699 

1  -    1.  609  347 

2 

6.561  667 

2 

0.  609  6012 

2        1.  242  7399 

2          3.  218  694 

3 

9.842500 

3 

0.9144018 

3        1.  864  1098 

'  3          4.  828  042 

4 

13.  123  333 

4 

1.  219  2024 

4        2.  485  4798 

4          6.437  389 

5 

16.404  166 

5 

1.  524  0030 

5        3.  106  8497 

5         8.  046  736 

6 

19.685  000 

6 

1.828  8037 

6        3.  728  2196 

6          9.  656  083 

7 

22.  965  833 

7 

2.  133  6043 

7        4.  349  5896 

7        11.265  430 

8 

26.246  666 

8 

2.  438  4049 

8        4.  970  9595 

8        12.  874  778 

9 

29.527  500 

9 

2.  743  2055 

9        5.  592  3295 

9        14.  484  125 

GEOGKAPHIC  TABLES  AND  FORMULAS. 

Table  of  corrections  to  longitude  for  difference  in  arc  and  sine. 


269 


logs(-) 

log  dif- 
ference. 

logAA(  +  ) 

logs  (-) 

•log  dif- 
ference. 

log  AX  (  +  ) 

logs(-) 

log  dif- 
ference. 

logAA(+) 

3.  876 

0.000  0001 

2.385 

4.871 

0.000  0098 

3.380 

5.  172 

0.  000  0392 

3.681 

4.026 

02 

2.535 

4.882 

103 

3.391 

5.178 

402 

3.687 

4.114 

03 

2.623 

4.892 

108 

3.401 

5.183 

412 

3.692 

4.177 

04 

2.686 

4.903 

114 

3.412 

5.188 

422 

3.697 

4.225 

05 

2.734 

4.913 

119 

3.422 

5.  193 

433 

3.702 

4.265 

06 

2.774 

4.922 

124 

3.431 

5.199 

443 

3.708 

4.298 

07 

2.807 

4.932 

130 

3.441 

5.204 

453 

3.713 

4.327 

08 

2.836 

4.941 

136 

3.450 

5.209 

464 

3.718 

4.353 

09 

2.862 

4.950 

142 

3.459 

5.214 

474 

3.723 

4.376 

10 

2.885 

4.959 

147 

3.468 

5.219 

486 

3.728 

4.396 

11 

2.905 

4.968 

153 

3.477 

5.223 

497 

3.732 

4.415 

12 

2.924 

4.976 

160 

3.485 

5.  228 

508 

3.737 

4.433 

13 

2.942 

4.985 

166 

3.494 

5.233 

519 

3.742 

4.449 

14 

2.958 

4.993 

172 

3.502 

5.238 

530 

3.747 

4.464 

15 

2.  973 

5.002 

179 

3.511 

5.  242 

541 

3.751 

4.478 

16 

2.987 

5.  010 

186 

3.519 

5.247 

553 

3.756 

4.491 

17 

3.000 

5.017 

192 

3.526 

5.251 

565 

3.760 

4.503 

18 

3.012 

5.025 

199 

3.534 

5.  256 

577 

3.765 

4.526 

20 

3.035 

5.033 

206 

3.542 

5.260 

588 

3.769 

4.548 

23 

3.057 

5.040 

213 

3.549 

5.  265 

600 

3.774 

.570 

25 

3.  079 

5.047 

221 

3.556 

5.  269 

613 

3.778 

.591 

27 

3.100 

5.054 

228 

3.563 

5.273 

625 

3.782 

.612 

30 

3.121 

5.062 

236 

3.571 

5.  278 

637 

3.787 

.631 

33 

3.140 

5.068 

243 

3.577 

5.  282 

650 

3.791 

.649 

36 

3.158 

5.075 

251 

3.584 

5.286 

663 

3.795 

.667 

39 

3.  176 

5.082 

259 

3.  591 

5.290 

674 

3.799 

.684 

42 

3.193 

5.088 

267 

3.597 

5.  294 

687 

3.803 

.701 

45 

3.210 

5.095 

275 

3.604 

5.299 

702 

3.808 

.716 

48 

3.225 

5.  102 

284 

3.611 

5.  303 

716 

3.812 

.732 

52 

3.241 

5.108 

292 

3.617 

5.307 

729 

3.816 

.746 

56 

3.255 

5.114 

300 

3.623 

5.  311 

743 

3.820 

.761 

59 

3.270 

5.120 

309 

3.629 

5.315 

757 

3.824 

.774 

63 

3.283 

5.  126 

318 

3.635 

5.319 

771 

3.828 

.788 

67 

2.297 

5.132 

327 

3.641 

5.323 

785 

3.832 

.801 

71 

3.310 

5.138 

336 

3.647 

5.327 

800 

3.836 

.813 

75 

3.322 

5.144 

345 

3.653 

5.331 

814 

3.840 

.825 

80 

3.334 

5.150 

354 

3.659 

5.335 

829 

3.844 

.834 

84 

3.343 

5.156 

364 

3.665 

5.239 

845 

3.848 

.849 

89 

3.358 

5.161 

373 

3.670 

5.343 

861 

3.852 

.860 

94 

3.369 

5.167 

383 

3.676 

5.347 

877 

3.856 

INVERSE    SOLUTION. 

HAVING   LATITUDES  AND   LONGITUDES  OF  Two   POINTS  TO   COMPUTE  AZIMUTHS  AND 

DISTANCES. 

The  following  example  shows  the  method  of  performing  the  opera- 
tion. The  northernmost  point  should  be  used  as  the  initial  position, 
then  all  signs  for  (I),  (II),  and  (III)  are  +,  and  for  (IV)  -.  The 
value  of  ^/A-  may  be  either  +  or  — ,  but  this  sign  need  only  be  used 
in  determining  in  which  quadrant  tfce  azimuth  angle  a  falls,  i.  e.,  the 
sign  of  tan  a  (12).  An  inspection  of  a  rough  plat  of  the  positions 
will  also  determine  this.  The  correction  to  A\  is  found  from  a 
distance  scaled  off  from  the  plat,  and  need  not  be  very  close.  In 
(8)  the  term  (I-f-11)2  is  the  square  of  the  difference  of  latitude  A<p  in 
seconds.  Since  (IV)  is  always  small,  log  (I)  in  (8)  may  be  taken  as 
log  of  A<p  from  (1).  If  cos  a  is  smaller  than  sin  <*,  find  s  from 
log  s  cos  a  in  (11).  As  a  check  on  the  work  compute  the  second 


GEOGRAPHIC  TABLES  AND  FORMULAS. 


position,  using  distance  and  azimuth  found  as  above.  The  order  of 
solution  is  shown  by  figures  in  parentheses.  The  cosines  of  latitudes 
are  proportional  to  the  intercepted  parallels. 


Latitude  =  9    =38°  23'    27"  .00  Given. 
<p'  =»  37    45    09   .30  Given. 

A<p    =-          38'    17"  .70 

=2297".  70  (1) 
log  A  <p  =  3.3612933 
log  C  =  1.30360 
log  82  sin2a  =  8.75770 

log      (II)          0.06130  (7) 

(II)     =  1"  .152 
log  D  =  2.3812 
log  (I  +  II)2  =•  6.7226 


log 


(III)  9.1038  (8) 

III      =  0"  .13 
log  E  =  6.0711 


log  I  =  3.3613 

log  IV  -  8.1901  (9) 

IV  =  -"  .02 

(II)  =  +  1.15" 

(III)  =--  +  0.13 

IV  =  -    .02 

Sum  =  +  1.26"  (10) 
A  <p  =  2297.70 

(I)  =  22%.44 


Longitude  =  A   =  104°  32'  48"  .20  Given 
A'  r=  104   49  05    .50  Given 

A  A  =  16'  17"  .30  + 

=  977"  .30  +  (2) 
log  A  A  =  2.9900279 

log  A  A  correction  =  +  16 
log  S  (scaled  distance)  correction  =  —  99 

(apply  with  opposite  sign)  —  83  (3) 
log  A  A'  =  2.9900362  (4) 

log  A'      =  8.5091750  (5) 
Sec  <p'     =  0.1020092 


8.6111842  (+) 
=  2.9900362  (+) 


log  A  A' 
log  S  sin  a 

log  S  COS  a 


4.3788520  (  +  )  (6) 
4.8500742  (+)  (11) 


=  tan  a  =  9.5287778  (12) 


log    (I) 
log  (B) 


3.3610475 
8.5109733 


log  S  COS  a  =  4.8500742  (11) 
Azimuth  =  a  -  18°  40'  10"  .8  (13) 
log  S  sin  a  =  4.3788520 
log  sin     a  =  9.5053013 


log  distance  =  log  S  =  4.8735507  (14) 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


271 


TABLE  24. — Log  m,  for  use  in  computing  spherical  excess. 
[Computed  for  the  Clarke  spheroid  of  1866.] 


Lat. 

Logm. 

Lat. 

Log  m. 

Lat. 

Logm. 

o   / 

0     / 

o    / 

0  00 

1.40695 

25  00 

1.40590 

50  00 

1.  40349 

0  30 

1.40695 

25  30 

1.  40586 

50  30 

1.  40344 

1  00 

1.40695 

26  00 

1.40582 

51  00 

1.  40339 

1  30 

1.  40694 

26  30 

1.  40578 

51  30 

1.  40334 

2  00 

1.40694 

27  00 

1.  40573 

52  00 

1.  40329 

2  30 

1.  40694 

27  30 

1.40569 

52  30 

1.  40324 

3  00 

1.40693 

28  00 

1.40565 

53  00 

1.  40319 

3  30 

1.40693 

28  30 

1.40560 

53  30 

1.40314 

4  00 

1.  40692 

29  00 

1.40556 

54  00 

1.  40309 

4  30 

1.  40691 

29  30 

1.  40552 

54  30 

1.  40304 

5  00 

1.  40690 

30  00 

1.40548 

55  00 

1.  40299 

5  30 

1.40689 

30  30 

1.  40544 

55  30 

1.  40295 

6  00 

1.  40688 

31  00 

1.  40539 

56  00 

1.40290 

6  30 

1.  40687 

31  30 

1.40534 

56  30 

1.  40285 

7  00 

1.  40686 

32  00 

1.40530 

57  00 

1.40280 

7  30 

1.40685 

32  30 

1.40525 

57  30 

1.  40276 

8  00 

1.40683 

33  00 

1.40520 

58  00 

1.  40271 

8  30 

1.40682 

33  30 

1.  40516 

58  30 

1.  40266 

9  00 

1.40680 

34  00 

1.  40511 

59  00 

1.  40262 

9  30 

1.40679 

34  30 

1.40506 

59  30 

1.  40257 

10  00 

1.40677 

35  00 

1.  40501 

60  00 

1.40253 

10  30 

1.40675 

35  30 

1.  40496 

60  30 

1.40249 

11  00 

1.40673 

36  00 

1.  40491 

61  00 

1.  40244 

11  30 

1.40671 

36  30 

1.  40486 

61  30 

1.  40240 

12  00 

1.40669 

37  00 

1.  40482 

62  00 

1.  40235 

12  30 

1.  40667 

37  30 

1.40477 

62  30 

1.40231 

13  00 

1.40665 

38  00 

1.  40472 

63  00 

1.  40227 

13  30 

1.40663 

38  30 

1.40467 

63  30 

1.  40223 

14  00 

1.40660 

39  00 

1.  40462 

64  00 

1.  40219 

14  30 

1.  40658 

39  30 

1.  40457 

64  30 

1.  40215 

15  00 

1.40655 

40  00 

1.  40452 

65  00 

1.  40210 

15  30 

1.40653 

40  30 

1.40446 

65  30 

1  .  40207 

16  00 

1.  40650 

41  00 

1.  40441 

66  00 

1.  40203 

16  30 

1.  40647 

41  30 

1.  40436 

66  30 

1.40199 

17  00 

1.40644 

42  00 

1.  40431 

67  00 

1.40195 

17  30 

1.40642 

42  30 

1.  40426 

67  30 

1.40192 

18  00 

1.40639 

43  00 

1.  40421 

68  00 

1.40188 

18  30 

1.40636 

43  30 

1.  40416 

68  30 

1.  40185 

19  00 

1.40632 

44  00 

1.  40411 

69  00 

1.  40181 

19  30 

1.  40629 

44  30 

1.40406 

69  30 

1.  40178 

20  00 

1.  40626 

45  00 

1.40400 

70  00 

1.  40174 

20  30 

1.40623 

45  30 

1.40395 

70  30 

1.40171 

21  00 

1.40619 

46  00 

1.  40390 

71  00 

1.  40168 

21  30 

1.  40616 

46  30 

1.  40385 

71  30 

1.  40164 

22  00 

1.  40612 

47  00 

1.40380 

72  00 

1.  40161 

22  30 

1.  40608 

47  30 

1.  40375 

23  00 

1.  40605 

48  00 

1.  40369 

23  30 

1.  40601 

48  30 

1.40364 

24  00 

1.  40597 

49  00 

1.  40359 

24  30 

1.  40594 

49  30 

1.  40354 

272 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


APPROXIMATE    SPHERICAL   EXCESS. 


This  may  be  obtained  by  dividing-  the  area  of  the  triangle  in  square 
miles  by  75.5. 

TABLE  25. — Mean  refraction. 


If 

%* 

Refraction. 

11 
as 
%* 

Refraction. 

p 
il 

S33 

3* 

Refraction. 

il 

fi 

Refraction. 

C!  & 

g-o 

II 
£« 

Refrac- 
tion. 

o  / 

00 

/       // 
34  54.1 

a 

124.9 
116.9 
108.8 
100.8 
92.9 
85  2 

0      / 

70 

/      n 
7  19.7 

n 
9.2 
8.8 
8.4 
8.2 
7.9 
7.6 
7.3 
7.1 
6.8 

O       1 

140 

/      // 
347.4 

n 
5.3 
5.1 
4.9 
4.7 
4.5 
4.3 
4.1 
4.0 
3.9 
3.7 
3.6 
3.5 
3.3 
3.2 
3.2 
3.0 
2.9 
2.9 
2  8 

o      /  • 

280 

/     // 
148.2 

// 

1.5 

o 

42 
43 

// 
64.0 
61.8 

n 
2.2 
2.1 
2.0 
2.0 
1.9 
1.9 
1.7 
1.8 
1.7 
1.6 
1.6 
1.6 
1.5 
1.5 
1.4 
1.4 
1.4 
1.4 
1.3 
1.3 
1.3 
1.2 
1.3 
1.2 
1.2 
1.2 
1.1 
1.2 
1.1 
1.1 
1.1 
1.1 
1.1 
1.0 
1.1 
1.1 
1.1 
1.0 
1.1 
1.0 
4.0 
4.1 

10 
20 
30 
40 
50 

32  49.2 
30  52.3 
29    3.5 
27  22.7 
25  49.8 

10 
20 
30 
40 
50 

710.5 
7    1.7 
653.3 
645.1 
637.2 

20 
40 

342.1 
337.0 

20 
40 

146.7 
145.3 

1.5 
1.4 
1.4 
1.3 
1.3 
1.3 
1.3 
1.3 
1.2 
1.2 
1.2 
1.1 
1.1 
1.1 
1.1 
1.1 
1.1 
1.0 
1.0 
1.0 
1.0 
1.0 
1.0 
0.9 
0.9 
0.9 
0.9 
0.9 
0.9 
0.9 
0.8 
0.9 
0.8 
0.8 
0.8 
0.8 
0.8 
0.8 
0.8 
0.7 

44 
45 
46 

59.7 
57.7 
55.7 

150 

332.1 

290 
20 
40 

1  43.8 

20 
40 

327.4 
322.9 

142.4 
1  41.0 

47 

48 
49 

53.8 
51.9 
50.2 

10 

24  24.6 

77.9 

80 

629.6 

160 

318.6 

300 

1  39.7 

10 
20 
30 
40 
50 

23    6.7 
21  55.6 
20  50.9 
1951.9 
18  58.0 

71.1 
64.7 
59.0 
53.9 
49.4 

10 
20 
30 
40 
50 

6  22.3 
615.2 
6    8.4 
6    1.8 
555.4 

20 
40 

314.5 
3  10.5 

20 
40 

1  38.4 
1  37.1 

50 
~ 
52 
53 

48.4 

6.6 
6.4 
6.1 
6.0 
5.7 
5.6 
5.6 

170 

3    6.6 

31  0    1  35.8 

46.7 
45.1 
43.5 

20 
40 

3    2.9 
259.3 

20 
40 

134.5 
133.3 

20 

18    8.6 

90 

549.3 

54 
55 
56 

41.9 
40.4 
38.9 

10 
20 
30 
40 
50 

17  23.0 
1640.7 
16    0.9 
15  23.4 

14  47.8 

45.6 
42.3 
39.8 
37.5 
35.6 

10 
20 
30 
40 
50 

543.3 
537.6 
532.0 
526.5 
521.3 

180 

2  55.8 

320 

1  32.1 

20 

40 

252.5 
249.3 

20 
40. 

130.9 
129.8 

57 
58 
59 
"60" 

37.5 
36.1 
34.7 
33.3 

190 

246.1 

330 

1  28.7 

5.1 
5.0 
4.8 
4.7 
4.5 
4.4 
4.3 
4.2 
4.1 
3.9 
3.9 
3.7 
3.7 
3.6 
3.4 
3.4 
3.3 
3.2 
3.2 
3.1 
3.0 
2.9 
2.9 
2.8 
2.8 

20 
40 

243.1 
240.2 

20 
40 

127.6 
126.5 

30 

14  14.6 

30  9 

100 

516.2 

10 
20 
30 
40 
50 

13  43.7 
13  15.0 
12  48.3 
1223.7 
12    0.7 

23.7 
26.7 
24.6 
23.0 
21.8 
20.6 
19.7 
19.0 
18.4 
17.9 
16.8 
15.6 
14.9 
14.1 
13.5 
12.8 
12.3 
11.7 
11.3 
10.8 
10.3 
10.0 
9.5 

10 
20 
30 
40 
50 

511.2 
5    6.4 
5    1.7 
457.2 

452.8 

200 

237.3 

340 

1  25.4 

61 
62 
63 

32.0 
30.7 
29.4 

20 
40 

234.5 
231.9 

2.6 
2.6 
2.5 
2.5 
2.4 
2.3 
2.2 
2.2 
2.2 
2.1 
2.0 
1.9 
1.9 
1.9 
1.8 
1.8 
1.8 
1.7 
1.7 
1.6 
1.6 
1.5 
1.5 

20 
40 

1  24.3 
1  23.3 

210 

229.3 

350 

122.3 

64 
65 
66 

28.2 
26.9 
25.7 

20    2  26.8 
40  1  2  24.3 

20 
40 

1  21.3 
1  20.3 

40 

11  38.9 

110 

448.5 

10 
20 
30 
40 
50 
50 

11  18.3 
10  58.6 
10  39.6 
10  21.2 
10    3.3 

10 
20 
30 
40 
50 

444.3 
440.2 
436.3 
432.4 

428.7 

220    221.9 

360 

1  19.3 

67 
68 
69 
"70" 
— 
72 
73 

24.5 
23.3 
22.2 

irnr 

19.9 
18.8 
17.7 

20    2  19.6 
40    2  17.4 

20 
40 

118.3 
1  17.4 

23  0    2  15.2 

370 

116.5 

946.5 

120 

425.0 

20 
40 

2  13.0 
210.9 

20 
40 

1  15.6 
114.7 

10 
20 
30 
40 
50 

930.9 
9  16.0 
9    1.9 
848.4 
8  35.6 

10 
20 
30 
40 
50 
130 

421.4 
418.0 
4  14.6 
411.3 
4    8.1 

240 

2    8.9 

380 

1  13.8 

74 
75 
76 

16.6 
15.5 
14.5 

20 
40 

2    7.0 
2    5.1 

20 
40 

1  12.9 
112.0 

250 

2    3.2 

39  0 

1  11.2 

77 
78 
79 

13.4 
12.3 

11.2 

60 

823.3 

4    4.9 

20 
40 

2    1.4 
159.6 

20 
40 

1  10.3 
1    9.5 

10 
20 
30 
40 
50 

811.6 
8    0.3 
749.5 
739.2 
729.2 

10 
20 
30 
40 
50 

4    1.8 
358.8 
355.9 
353.0 
350.2 

260 

1  57.8 

400 

1    8.7 

80 

10.2 

20 
40 

156.1 
1  54.4 

20 
40 

1    7.9 
1    7.1 

"8T 
82 
86 
90 

9.1 
8.1 
4.1 
0.0 

270 

1  52.8 

41  0 

1    6.3 

70 

719.7 

140 

347.4 

20 
40 

151.2 
149.7 

20 
40 

1    5.5 
1    4.7 

280 

148.2 

420 

1    4.0 

GEOGRAPHIC    TABLES    AND   FORMULAS.  273 

TABLE  26. — Corrections  for  currofurc  and  refraction,  in  fed— 0.574  (distance,  miles}2. 
[Difference  in  feet  between  the  apparent  and  true  level  at  distances  varying  from  1  to  66  miles.] 


Distance, 
miles. 

Difference  in  feet  for  — 

Distance, 
miles. 

Difference  in  feet  for— 

Curvature. 

Refrac- 
•     tion. 

Curvature 
and 
refraction. 

Curvature. 

Refrac- 
tion. 

Curvature 
and 
refraction. 

1 

0.7 

0.1 

0.6 

34 

771.3 

108.0 

663..  3 

2 

2.7 

0.4 

2.3 

35 

817.4 

114.4 

703.0 

3 

6.0 

0.8 

5.2 

36 

864.8 

121.1 

743.7 

4 

10.7 

1.5 

9.2 

37 

913.5 

127.9 

785.6 

5 

16.7 

2.3 

14.4 

38           963.  5 

134.9 

828.6 

6 

24.0 

3.4 

20.6 

39 

1,014.9 

142.1 

8.72.  s 

7 

32.7 

4.6 

28.1 

40 

1,067.6 

149.5 

918.1 

8 

42  7 

6.0 

36.7 

41 

1,121.7 

157.0 

964.7 

9 

54.0 

7.6 

46.4 

42 

1,177.0 

164.8 

1,012.2 

10 

66.7 

9.3 

57.4 

43 

1,233.7 

172.7 

1,061.0 

11 

80.7 

11.3 

69.4 

44 

1,  291.  8 

180.8 

1,111.0 

12 

96.1 

13.4 

82.7 

45 

1,351.2 

189.2 

1,162.0 

13 

112.8 

15.8 

97.0 

46 

1,411.9 

197.7 

1,214.2 

14 

130.8 

18.3 

112.5 

47 

1,474.0 

206.3 

1,  267.  7 

15 

150.1 

21.0 

129.1 

48 

1,537.3 

215  2 

1,  322.  1 

16 

170.8 

23.9 

146.9 

49 

1,  602.  0 

224.3 

1,377.7 

17 

192.8 

27.0 

165.8 

50 

1,668.1 

233.  5 

1,  434.  6 

18 

216.  2 

30.3 

185.9 

51 

1,  735.  5 

243.0 

1,  492.  5 

19 

240.9 

33.7 

207.2 

52 

1,  804.  2 

252.6 

1,  551.  6 

20 

266.9 

37.4 

229.5 

53 

1,874.3 

262.4 

1,611.9 

21 

'    294.3 

41.2 

253.1 

54 

1,  945.  7 

272.4 

1,673.3 

22 

322.  9 

45.2 

277.7 

55 

2,  018.  4 

282.6 

1,735.8 

23 

353.  0 

49.4 

303.  6 

56 

2,  092.  5 

292.9 

1,  799.  6 

24 

384.  3 

53.8 

330.5 

57 

2,  167.  9 

303.5 

1,864.4 

25 

417.0 

58.4 

358.6 

58 

2,  244.  6 

314.2 

1,930.4 

26 

451.1 

63.1 

.  388.0 

59 

2,322.7 

325.2 

1,  997.  5 

27 

486.4 

68.1 

418.3 

60 

2,  402.  1 

336.3 

2,  065.  8 

28 

523.  1         73.  2 

449.9 

61 

2,  482.  8 

347.  6       2,  135.  2 

29 

561.2     •     78.6           482.6 

62 

2,  564.  9 

359.1 

2,  205.  8 

30 

600.  5         84.  1           516.  4 

63 

2,  648.  3 

370.8 

2,  277.  5 

31 

641.2         89.8           551.4 

64 

2,  733.  0 

382.6 

2,  350.  4 

32 

'  683.  3 

95.7 

587.6 

65 

2,  819.  1 

394.7 

2,  424.  4 

33 

726.6 

101.7 

624.9 

66 

2,906.5 

406.9 

2,  499.  6 

46061—08 18 


274  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — FOR   OBTAINING    DIFFERENCES   OF  ALTITUDE   FOR  ANY  MINUTE   UP   TO    15 
DEGREES,  AND  FOR  ANY  DISTANCE. 

[Prepared  by  Arthur  P.  Davis.] 
EXPLANATION    OF   TABLE. 

The  left-hand  column  is  the  minutes  of  the  vertical  angle,  the 
degrees  being  denoted  by  the  large  number  at  top  of  page.  The  bold- 
face figures  at  top  of  column  is  the  distance  in  miles.  Numbers  in  the 
body  of  the  table  denote  the  difference  of  elevation  corresponding  to 
the  angle  on  the  left  and  the  distance  at  top.  The  correction  for 
curvature,  refraction,  and  height  of  instrument  is  always  plus;  it  there- 
fore increases  the  difference  of  level  for  angles  of  elevation,  and  is 
subtracted  from  the  difference  of  level  for  angles  of  depression. 

Example.—  Required  the  difference  of  altitude  corresponding  to  a 
vertical  angle  of  -f  9°  18'  at  a  distance  of  3.628  miles.  On  page  284 
the  tabular  number  corresponding  to  9°  18'  and — 

Feet. 

A.  distance  of  3  mites  is 2,  594 

For  a  distance  of  6  miles  is  5, 188 — for  0.6  is  therefore 519 

For  a  distance  of  2  miles  is  1,729 — for  0.02  is  therefore 17 

For  a  distance  of  8  miles  is  6,917— for  0.008  is  therefore 7 

Correction  for  curvature,  refraction,  and  height  of  instrument  for  3.6  miles  is  -f  -         12 

Total  difference  of  altitude -f  3, 149 


GEOGRAPHIC    TABLES    AND    FORMULAS.  275 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

0° 


1 

2 

3 

* 

5 

6 

7 

8 

9 

Corrections  for  curva- 
ture, refraction,  and 
height  of  instruments 

1 

1.5 

3.1 

5 

6 

8 

9 

11 

12 

14 

Miles. 

•Feet. 

Miles. 

Feet. 

2 

3.1    6.1 

9 

12 

15 

18 

22 

25 

28 

1.6 

6 

10.2 

64 

3 

4.6    9.2 

14 

18 

23 

28 

32 

37 

41 

2.1 

7 

10.3 

65 

4 

6.1   12.3 

18 

25 

31 

37 

43 

49 

55 

2.5 

8 

10.4 

67 

5 

7.7  i  15.4 

23 

31 

38 

46 

54 

61 

69 

2.8 

9 

10.5 

68 

6 

9.2   18.4 

28 

37 

46 

55 

65 

74 

83 

3.1 

10 

10.6 

69 

7 

10.8   21.5 

32 

43 

54 

65 

75 

86 

97 

3.4 

11 

10.7 

70 

8 

12.3   24.6 

37 

49 

61 

74 

86 

98 

111 

3.6 

12 

10.8 

71 

9 

13.8   27.6 

*   41 

55 

69 

83 

97 

111 

124 

3.8 

13 

10.9 

73 

10 

15.  4   30.  7 

46 

61 

77 

92 

108 

123 

138 

4.1 

14 

11.0 

74 

11 

16.9   33.8 

51 

68 

84 

101 

118 

135 

152 

4.3 

15 

11.1 

75 

12 

18.4 

36.9 

56 

74 

92 

111 

129 

147 

166 

4.5 

16 

11.2 

77 

13 

20.0 

39.9 

60 

80 

100 

120 

140 

160 

180 

4.7 

17 

11.3 

78 

14 

21.5 

43.0 

65 

86 

108 

129 

151 

172 

194 

4.8 

18 

11.4- 

79 

15 

23.0 

46.1 

69 

92 

115 

138 

161 

184 

207 

5.0 

19 

11.5 

80 

16 

24.6 

49.1 

74 

98 

123 

147 

172 

197 

221 

5.2 

20 

11.6 

82 

17 

26.1 

52.2 

78 

104 

131 

157 

183 

209 

235 

5.4 

21 

11.7 

83 

is    27.6 

55.3 

83 

111 

138 

"  166 

194 

221 

249 

5.5 

22 

11.8 

84  ! 

19    29.2 

58.4 

88 

117 

146 

175 

204 

233 

263 

5.7 

23 

11.9 

86 

20    30.7 

61.4 

92 

123 

154 

184 

215 

246 

276 

5.8 

24 

12.0 

87 

21    32.  3 

64.5 

97 

129 

161 

194 

226 

258 

290 

6.0 

25 

12.1 

89 

22    33.  8 

67.6 

101 

135 

169 

203 

237 

270 

304 

6.1 

26 

12.2 

90 

23    35.3 

70.7 

106 

141 

177 

212 

247 

283 

318 

6.3 

27 

12.3 

91 

24    36.9 

73.7 

111 

147 

184 

221 

258 

295 

332 

6.4 

28 

12.4 

93 

25    38.  4 

76.8 

115 

154 

192 

230 

269 

307 

346 

6.5 

29 

12.5 

94 

26 

39.9 

79.9 

120 

160 

200 

240 

280 

319 

359 

6.7 

30 

12.6 

96 

27 

41.5 

82.9 

124 

166 

207 

249 

290 

332 

373 

6.8 

31 

12.7 

97 

28 

43.0 

86.0 

129 

172 

215 

258 

301 

344 

387 

6.9 

32 

12.8 

99 

29 

44.5 

89.1 

134 

178 

223 

267 

312 

356 

401 

7.0 

33 

12.9 

100 

30 

46.1 

92.2 

138 

184 

230 

276 

323 

369 

415 

7.2 

34 

13.0 

102 

31 

47.6 

95.2 

143 

190 

238 

286 

333 

381 

429 

7.3 

35 

13.1 

103 

32    49.  2 

98.3 

147 

197 

246 

295 

344 

393 

442 

7.4 

36 

13.2 

105 

33    50.7 

101.4 

152 

203 

253 

304 

355 

405 

456 

7.5 

37 

13.3 

106 

34 

52.  2 

104.4 

157 

209 

261 

313 

366 

418 

470 

7.6 

38 

13.4 

108 

35 

53.8 

107.5 

161 

215 

269 

323 

376 

430 

484 

7.8 

39 

13.5 

109 

36    55.3 

110.6 

166 

221 

276 

332 

387 

442 

498 

7.9 

40 

13.6 

111 

37    56.8 

113.7 

170 

227 

284 

341 

398 

456 

512 

8.0 

41 

13.7 

112 

38    68.4 

116.7 

175 

233 

292 

350 

409 

467 

525 

8.1 

42 

13.8 

114 

39    59.9 

119.8 

180 

240 

300 

359 

419 

479 

539 

8.2 

43 

13.9. 

115 

40 

61.4 

122.9 

184 

246 

307 

369 

430 

492 

553 

8.3- 

44 

14.0 

117 

41 

63.0 

125.9 

189 

252 

315 

378 

441 

504 

567   8*74 

45 

14.1 

119 

42 

64.5 

129.0 

194 

258 

323 

387 

452 

516 

581   8.5 

46 

14.2 

120 

43 

66.0 

132.1 

198 

264 

330 

396 

462 

528 

594  !  8.6 

47 

14.  3 

122 

44 

67.6 

135.2 

203 

270 

338 

405 

473 

541 

608 

8.7 

48 

14.4 

124 

45 

69.1 

138.2 

207 

276 

346 

415 

484 

553 

622 

8.8 

49 

14.5 

125 

46 

70.6 

141.3 

212 

283 

353 

424 

495 

565 

636 

8.9 

50 

14.6 

127 

47 

72.2 

144.4 

217 

289 

361 

433 

505 

578 

650 

9.0 

51 

14.7 

129 

48 

73.7 

147.  5 

221 

295 

369 

442 

516 

590 

664 

9.1 

52 

14.8 

130 

49 

75.3 

150.5 

226 

301 

376 

452 

527 

602 

677 

9.2 

53 

14.9 

132 

50 

76.8 

153.6 

230 

307 

384 

461 

538 

614 

691 

9.3 

54 

15.0 

134 

51 

78.3 

156.7 

235 

313 

392 

470 

548 

627 

705 

9.4 

55 

15.1 

135 

52 

79.9 

159.7 

240 

319 

399 

479 

559 

639 

719 

9.5 

56 

15.2 

137 

53 

81.4 

162.8 

244 

326 

407 

488 

570 

651 

733 

9.6 

58 

15.3 

139 

54 

82.9 

165.9 

249 

332 

415 

498 

581 

664 

747   9.  7 

59 

15.4 

141 

55 

84,5 

169.0 

253 

338 

422 

507 

591 

676 

760   9.8 

60 

15.5 

142 

56 

86.0 

172.  0 

258 

344 

430 

516 

602 

688 

774- 

9.9 

61 

15.6 

144 

67 

87.5 

175.1 

263 

350 

438 

525 

613 

700 

788 

10.0 

62 

15.7 

146 

58 

89.1 

178.2 

267 

356 

445 

535 

624 

713 

802 

10.1 

63 

15.8 

148 

59 

90.6 

181.3 

272 

363 

453 

544 

634 

725 

816 

15.9 

160 

16.0 

151 

CO    92.2 

184.3 

276 

369 

461 

553 

645 

737 

829 

« For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


276  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

1° 


1 

2 

3 

4 

5 

6 

8 

9 

Corrections  for  curva- 
ture, refraction,  and 
height  of  instruments 

0 

92.2 

184.3 

276 

369 

461 

553 

645 

737 

829 

Miles. 

Feet. 

Miles. 

Feet. 

1 

93.7 

187.4 

281 

375 

468 

562 

656 

750, 

843 

16.1 

153 

22.1 

285 

2 

95.2 

190.5 

286 

381 

476 

571 

667 

762 

857 

16.2 

155 

22.2 

287 

3 

96.8 

193.5 

290 

387 

484 

581 

677 

774 

871 

16.3 

157 

22.3 

290 

4 

98.  3  196.  6 

295 

393 

.  492 

590 

688 

786 

885 

16.4 

159 

22.4 

293 

5 

99.8  j  199.7 

300 

399 

499 

599 

699 

799 

899 

16.5 

161 

22.5 

295 

6 

101.4  !  202.8 

304 

406 

507 

608 

710 

811 

912 

16.6 

163 

22.6 

298 

7 

102.  9  205.  8 

309 

412 

515 

618 

720 

823 

926 

16.7 

165 

22.7 

300 

8 

104.  4  208.  9 

313 

418 

522 

627 

731 

836 

940 

16.8 

167 

22.8 

303 

9 

106.0  212.0 

318 

424 

530 

636 

742 

848 

954 

16.9 

168 

22.9 

306 

10 

107.5  215.1 

323 

430 

538 

645 

-  753 

860 

968 

17.0 

170 

23.0 

308 

11 

109.1  218.1 

327 

436 

545 

654 

763 

873 

982 

17.1 

172 

23.1 

311 

12 

110.6  221.2 

332 

442 

553 

664 

774 

885 

995 

17.2 

174 

23.2 

313 

13 

112.1  ±21.:; 

336 

449 

561 

673 

785 

897 

1,009 

17.3 

176 

23.3 

316 

14 

113.7  227.3 

341 

455 

568 

682 

796 

909 

1,023 

17.4 

178 

23.4 

319 

15 

115.  2  230.  4 

346 

461 

576 

691 

806 

922 

1,037 

17.5 

180 

23.5 

321 

16 

116.  7  233.  5 

350 

467 

584 

700 

817 

934 

1,051 

17.6 

182 

23.6 

324 

17 

118.3 

236.  6 

355 

473 

591 

710 

828 

946 

1,065 

17.7 

184 

23.7 

327 

18 

119.8 

239.6 

359 

479 

599 

719 

839 

959 

1,078 

17.8 

186 

23.8 

330 

19 

121.4 

242.  7 

364 

485 

607 

728 

849 

971 

1,092 

17.9 

188 

23.9 

332 

20 

122.9 

245.8 

369 

492 

614 

737 

860 

983 

1,106 

18.0 

190 

24.0 

335 

21 

124.4 

248.9 

373 

498 

622 

747 

871 

995 

1,120 

18.1 

193 

24.1 

338 

22 

126.  0 

251.9 

378 

504 

630 

756 

882 

,008 

1,134 

18.2 

195 

24.2 

341 

23 

127.5 

2o5.  0 

383 

510 

638 

765 

893 

,020 

1,148 

18.3 

197 

24.3 

343  ! 

24 

129.0 

258.  1 

387 

516 

645 

774 

903 

,032 

1,161 

18.4 

199 

24.4 

346 

25 

130.6 

261.2 

392 

522 

653 

783 

914 

,045 

1,175 

18.5 

201 

24.5 

349 

26 

132.1 

264.2 

396 

528 

661 

793 

925 

,057 

1,189 

18.6 

203 

24.6 

352 

27 

133.6 

267.  3 

401 

535 

668 

802 

936 

,069 

1,  203 

18.7 

205 

24.7 

355 

28 

135.2 

270.4 

406 

541 

676 

811 

946 

,082 

1,217 

18.8 

207 

24.8 

358 

29 

136.  7 

273.5 

410 

547 

684 

820 

957 

,094 

1,231 

18.9 

210 

24.9 

360 

30 

138.3 

276.5 

415 

553 

691 

'  830 

968 

,106 

1,244 

19.0 

212 

25.  0   363 

31 

139.8 

279.6 

419 

559 

699 

839 

979 

,118 

1,258 

19.1 

214 

25.  1   366 

32 

141.  3 

282.7 

424 

565 

707 

848 

989 

,131 

1,272 

19.2 

216 

25.2   369 

33 

142.9 

285.7 

429 

571 

714 

857 

,000 

,143 

1,286 

19.3 

218 

25.3 

372 

34 

144.4 

288.8 

433 

578 

722 

866 

,011 

,155 

1,300 

19.4 

221 

25.4 

375 

35 

146.0 

291.  9 

438 

584 

730 

876 

,022 

,168 

1,314 

19.5 

223 

25.5 

378 

36 

147.5 

295.0 

442 

590 

737 

885 

,032 

,180 

1,327 

19.6 

225 

25.6 

381 

37 

149.0 

298.0 

447 

596 

745 

894 

,043 

,192 

1,341 

19.7 

227 

25.7 

384 

38 

150.6 

301.1 

452 

602 

753 

903 

,054 

.204 

1,355 

19.8 

230 

25.8 

387 

39 

152.1 

304.2 

456 

608 

760 

913 

,065 

,217 

1,369 

19.9 

232 

25.9 

390 

40 

153.6 

307.3 

461 

615 

768 

922 

,075 

,229 

1,383 

20.0 

234 

26.0 

393 

41 

155.2 

310.3 

466 

621 

776 

931 

,086 

,241 

1,397 

20.1 

236 

26.2 

399 

42 

156.7 

313.4 

470 

427 

784 

940 

,097 

,254 

1,410 

20.2 

239 

26.4 

405 

43 

158.  2 

316.  5 

475 

633 

791 

949 

,108 

,266 

1,424 

20.3 

241 

26.6 

411 

44 

159.8 

319.6 

479 

639 

799 

959 

,118 

,278 

1,438 

20.4 

243 

26.8 

417 

45 

161.3 

322.6 

484 

645 

807 

968 

,129 

,291 

1,452 

20.5 

246 

27.0 

423 

46 

162.9 

325.  7 

489 

651 

814 

977 

,140 

,303 

1,466 

20.6 

248 

27.2 

429 

47 

164.4 

328.8 

493 

658 

822 

986 

,151 

,315 

1,480 

20.7 

250 

27.4 

435 

48 

165.  9 

331.9 

498 

664 

830 

996 

,  162  . 

,327 

1,493 

20.8 

253 

27.6 

442 

49 

167.5 

334.9 

502 

670 

837 

1,005 

1,172 

,340 

1,5C7 

20.9 

255 

27.8 

448 

50 

169.0 

338.0 

507 

676 

845 

1,014 

1,183 

,352 

1,  521 

21.0 

258 

28.0 

455 

51 

170.6 

341.1 

512 

682 

853 

1,023 

1,194 

,364 

1,535 

21.1 

260 

28.2 

461 

52 

172.1 

344.2 

516 

688 

860 

1,032 

1,  205 

,377 

1,549 

21.2 

262 

28.4 

467 

53 

173.6 

347.2 

521 

694 

868 

1,042 

1,215 

,38i> 

1,563 

21.3 

265 

28.6 

474 

54 

175.2 

350.3 

525 

701 

876 

1,  051 

1,226 

,401 

1,576 

21.4 

267 

28.8 

480 

55 

176.7 

353.4 

530 

707 

883 

1,060 

1,237 

,414 

1,590 

21.5 

270 

29.0 

487 

56 

178.2 

356.5 

535 

713 

891 

1,069 

1,248 

,426 

1,604 

21.6 

272 

29.2 

494 

57 

179.8 

359.5 

539 

719 

899 

1,079 

1,258 

,438 

1,618 

21.7 

275 

29.4 

501 

58 

181.3 

362.6 

544 

725 

907 

1,088 

1,269 

,450 

1,632 

21.8 

277 

29.6 

507 

59 

182.  8 

365.7 

549 

731 

914 

1,097 

1,280 

,465 

1,643 

21.9 

280 

29.8 

514 

60 

184.4 

368.8 

553 

738 

922 

1,106 

1,291 

1,475 

1,659 

22.0 

282 

30.0 

521  j 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  277 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 


1 

2 

3 

* 

5 

6 

7 

8 

9 

Corrections  for  curva- 
ture, refraction,   and 
height  of  instruments 

0 

184.4 

368.8 

553 

738 

922 

1,106 

1,291 

1,475 

,659 

1 

185.9 

371.8 

558 

744 

930 

1,116 

1,301 

1,487 

,673 

Miles. 

Feet. 

M-tte*. 

Feet. 

2 

187.5 

374.9 

562 

750 

937 

1,125 

1,312 

1,500 

,687 

1.6 

6 

10.2 

64 

3 

189.0 

378  0 

567 

756 

945 

,134 

1,323 

1,512 

,701 

2.1 

7 

10.3 

65 

4 

190.5 

381.1 

572 

762         953 

,143 

1,334 

1,524 

,715 

2.5 

8 

10.4 

67 

5 

192.1 

384.1 

576 

768 

960 

,152 

1,344 

1,537 

,729 

2.8 

9 

10.5 

68 

6 

193.6 

387.2 

581 

774 

968 

,162 

1,355 

1,549 

,742 

3.1 

10 

10.6 

69 

7 

195.1 

390.3 

585 

781 

976 

,171 

1,366 

1,561 

,756 

3.4 

11 

10.7 

70 

8 

196.7 

393.4 

590 

787 

983 

,180 

1,377 

1,573 

,770 

3.6 

12 

10.8 

71 

9 

198.2 

396.4 

595 

793 

991 

,189 

1,388 

1,586 

,784 

3.8 

13 

10.9 

73 

10 

199.8 

399.5 

599 

799 

999 

,199 

1,398 

1,598 

1,798 

4.1 

14 

ii.o 

74 

11 

201.3 

402.6 

604 

805 

1,006 

,208 

1,409 

1,610 

1,812 

4.3 

15 

11.1 

75 

12 

202.8 

405.7 

609 

811 

1,014 

,217 

1,420 

1,623 

1,826 

4.5 

16 

11.2 

77 

13 

204.4 

408.8 

613 

818 

1,022 

,226 

1,431 

1,635 

1,839 

4.7 

17 

11.3 

78 

14 

205.9 

411.8 

618 

824 

1,030 

,235 

1,441 

1,647 

1,853 

4.,H 

18 

11.4 

79 

15 

207.5 

414.9 

622 

830 

1,037 

,245 

1,452 

1,660 

1,867 

5.0 

19 

11.  5 

80 

16 

209.0 

418.0 

627 

836 

1,045 

,254 

1,463 

1,672 

1,881 

5.2 

20 

11.6 

82 

17 

210.  5 

421.1 

632 

842 

1,053 

,263 

1,474 

1,684 

1,895 

5.4 

21 

11.7 

83 

18 

212.1 

424.1 

636 

848 

1,060 

,272 

1,484 

1,697 

1,909 

5.5 

22 

11.8 

84 

19 

213.6 

427.2 

641 

854 

1,068 

,282 

1,  495 

1,709 

1,932 

5.7 

23 

11.9 

86 

20 

215.1 

430.3 

645 

861 

1,076 

,291 

1,506 

1,721 

1,936 

5.8 

24 

12.0 

87 

21 

216.7 

650 

867 

1,083 

,300 

1,517 

1,733 

1,950 

6.0 

25 

12.1 

89 

22 

218.  2 

436.4 

655 

873 

1,091 

,309 

1,528 

1,746 

1,964 

6.1 

26 

12.2 

90 

23 

219.8 

439.5 

659 

879 

1,099 

,319 

1,538 

1,758 

1,978 

6.3 

27 

12.3 

91 

24 

221.3     442.6 

664 

885 

1,106 

,328 

1,549 

1,770 

1,  992 

6.4 

28 

12.4 

93 

25 

222.8  !  445.7 

669 

891 

1,114 

,337 

1,560 

1,783 

2,006 

6.5 

29 

12.5 

94 

26 

224.4 

448.7 

673 

897 

1,122 

,346 

1,571 

,  795 

2,  019 

8,7 

30 

12.6 

96 

27 

225.9 

451.8 

678 

904 

1,130 

,  355 

1,581 

,807 

2,  033 

6.8 

31 

12.7 

97 

28 

227.5 

454.9 

682 

910 

1,  137 

,365 

1,592 

,820 

2,047 

6.9 

32 

12.8 

99 

29 

229.0 

458.0 

687 

916 

1,145 

,374 

1,603 

,832 

2,061 

7.0 

33 

12.9 

100 

30 

230.5 

461.1 

692 

922 

1,153 

,383 

1,614 

,844 

2,  075 

7.2 

34 

13.0 

102 

31 

232.1 

464.1 

696 

928 

1,160 

,392 

1,624 

,857 

2,089 

7.3 

35 

13.1 

103 

32 

233.6 

467.2 

701 

934 

1,168 

,402 

1,635 

,869 

2,  102 

7.4 

90 

13.2 

105 

33 

235.1 

470.3 

705 

941 

1,176 

,411 

1,646 

,881 

2,  116 

7.5 

37 

13.3 

10(1 

34 

236.7 

473.4 

711 

947 

1,183 

,420 

1,1  '.57 

,893 

2,130 

7.6 

38 

13.4 

108 

35 

238.2 

476.4 

715 

953 

1,191 

,429 

1,668 

,906 

2,  144 

7.8 

39 

13.5 

109 

36 

239.8 

479.5 

719 

959 

1,199 

,439 

1,678 

,918 

2,158 

7.9 

40 

13.6 

111 

37 

241.3 

482.6 

724 

965 

1,207 

,  448 

1,689 

,930 

2,172 

8.0 

41 

13.7 

112 

38 

242.  8 

485.7 

729 

971 

1,214 

,457 

1,700 

,943 

2,186 

8.1 

42 

13.8 

114 

39 

244.4 

488.8 

733 

978 

1,  222 

,466 

1,711 

,955 

2,199 

8.2 

43 

13.9 

115 

40 

245.  9 

491.8 

738 

984 

1  ,  230 

,476 

1,721 

,967 

2,213 

8.3 

44 

14.0 

117 

41 

'_'  1  7  5 

494.9 

742 

990 

1,237 

,485 

1,732 

,980 

2,227 

8.4 

46 

14.1 

119 

42 

249.0 

497.0 

747 

996 

1,245 

,494 

1.743 

,992 

2,  241 

8.5 

46 

14.2 

120 

48 

250.5 

501.1 

752 

1,002 

1,253 

.5(i:;     ].75l 

2,004 

2,255 

8.6 

47 

14.3 

122 

44       252.  1 

504.2 

756 

,008 

1,260 

,612 

1,765 

2,017 

2,  269 

8.7 

48 

14.4 

124 

45       253.  6 

507.  2 

761 

,014 

1,268 

,  522 

1,775 

2,029 

2,283 

8.8 

49 

11.5 

125 

4fi 

255.  2 

510.  3 

765 

,021 

1  ,  276 

,531 

1,786 

2,041 

2,296 

8.9 

50 

14.6 

127 

47 

256.7 

513.  4 

770 

,027 

1,283 

,540 

1,797 

2,054 

2,310 

9.0 

51 

11.7 

129 

48 

258.2 

516.5 

775 

,033 

1,291 

,549 

1,808 

2,066 

2,  324 

9.1 

52 

14.8 

130 

49 

259.  8 

519.5 

779 

,039 

1,299 

,559 

1,818 

2,078 

2,338 

9.2 

53 

14.9 

132 

50 

261.3 

522.6 

784 

,045 

1,307 

,568 

1,829 

2,091 

2,352 

9.3 

54 

15.0 

134 

51 

262.9 

525.  7 

789 

,051 

1,314 

,577 

1,840 

2,103 

2,366 

9.4 

55 

15.1 

135 

52 

264.4 

528.  8 

793 

,058 

1,322 

,586 

1,851 

2,  115 

2,380 

9.5 

56 

15.2 

137 

53 

265.9 

531.9 

798 

,064 

1,330 

,596 

1,862 

2,  127 

2,393 

9.6 

58 

15.3 

139 

54 

267.  5     534.  9 

802 

,070 

1,337 

,605 

1,872 

2,  140 

2,  407 

9.7 

59 

15.4 

141 

55 

269.0 

538.0 

807 

,076 

1,345 

,614 

1,883 

2,152 

2,421 

9.8 

60 

15.5 

142 

56 

270.  6 

541.1 

812 

,082 

1,353 

(i'*:'i 

1,894 

2,164 

2,435 

9.9 

61 

15.6 

144 

57 

272.  1 

544.2 

816 

,088 

1,360 

,633 

1,905 

2,177 

2,449 

10.0 

52 

15.7 

146 

58 

273.6 

547.  3 

821 

,095 

1,368 

,642 

1,915 

2,189 

2,  463 

10.1 

63 

15.8 

148 

275.2 

550.3 

826 

,101 

1,376 

,  (151 

1,926 

2,  201 

2,477 

15.9 

1.50 

16,0 

151 

60 

276.7 

553.4 

830 

1,107 

1,384 

1,660 

1,937 

2,214 

2,490 

«  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


278  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

3° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections  for  curva- 
ture, refraction,  and 
height  of  instrument.** 

0 

276.7 

553.4 

830 

1,107 

1,384 

1,660 

1,937 

2,  214 

2,490 

Miles. 

Feet. 

1 

278.  3 

556.5 

835 

1,113 

1,391 

1,670 

1,948 

2,226 

2,  504 

10.1 

63 

2 

279.  8 

559.6 

839 

1,119 

1,  399 

1,679 

1,959 

2,  238 

2,518 

10.2 

64 

3 

281.3 

562.7 

844 

1,  125 

1,407 

1,688 

1,969 

2,  251 

1,532 

10.3 

65 

4 

282.9 

565.7 

849 

1,131 

1,414 

,697 

1,980 

2,263 

2,546 

10.4 

67 

5 

284.4 

568.8 

853 

1,138 

1,422 

,706 

1,991 

2,275 

2,560 

10.5 

68 

6 

286.0 

571.9 

858 

1,144 

1,430 

,716 

2,002 

2,  288 

2,574 

10.6 

69 

7 

237.5 

575.0 

862 

1,150 

1,437 

,725 

2,012 

2,300 

2,587 

10.7 

70 

8 

289.0 

578.1 

867 

1,156 

1,445 

,734 

2,023 

2,  312 

2,601 

10.8 

71 

9 

290.6 

581.2 

872 

1,  162 

1,453 

,743 

2,034 

2,  325 

2,615 

10.9 

73 

10 

292.1, 

584.2 

876 

1,168 

1,461 

1,753 

2,045 

2,337 

2,  629 

11.0 

75 

11 

293.7 

587  3 

881 

1,175 

1,468 

,762 

2,  056 

2,349 

2,643 

11.2 

77 

12 

295.2 

590.4 

886 

1,181 

1,576 

,771 

2,  066 

2,362 

2,657 

11.4 

79 

13 

296.7 

593.5 

890 

1,187 

1,484 

,780 

2,077 

2,373 

2,671 

11.6 

82 

14 

298.3 

596.6 

895 

1,193 

1,491 

,790 

2,088 

2,386 

2,685 

11.8 

84 

15 

299.8 

599.6 

899 

1,199 

1,499 

,799 

2,099 

2,399 

2,698 

12.0 

87 

16 

301.4 

602.7 

904 

1,205 

1,507 

,808 

2,110 

2,411 

2,  712 

12.2 

90 

17 

302.9 

605.8 

909 

1,212 

1,515 

,817 

2,120 

2,  423 

2,726 

12.4 

93 

18 

304.4 

608.9 

913 

1,  218 

1,522 

,827 

2,131 

2,436 

2,740 

12.6 

96 

19 

306.0 

612.0 

918 

1,224 

1,530 

,836 

2,142 

2,  448 

2,754 

12.8 

99 

20 

307.5 

615.0 

923 

1,230 

1,538 

,845 

2,153 

2,460 

2,768 

13.0 

102 

21 

309.1 

618.1 

927 

1,236 

1,545 

,854 

2,163 

2,  473 

2,  782 

13.2 

105 

22 

310.6 

621.2 

932 

1,242 

1,553 

,864 

2,174 

2,485 

2,795 

13.4 

108 

23 

312.1 

624.  3 

936 

1,249 

1,  561 

,873 

2,185 

2,497 

2,809 

13.6 

111 

24 

313.7 

627.4 

941 

1,255 

1,568 

,882 

2,196 

2,510 

2,823 

13.8 

114 

25 

315.  2 

930.5 

946 

1,  261 

1,576 

,891 

2,207 

2,  522 

2,837 

14.0 

117 

26 

316.8 

633.5 

950 

1,267 

1,584 

,901 

2,  217 

2,534 

2,851 

14.2 

120 

27 

318.3 

636.6 

955 

1,273 

1,592 

,910 

2,  228 

2,547 

2,865 

14.4 

124 

28 

319.9 

639.7 

960 

1,279 

1,599 

,919 

2,240 

2,559 

2,879 

14.6 

127 

29 

321.  4 

642.7 

964 

1,286 

1,607 

,928 

2,250 

2,571 

2,893 

14.8 

130 

30 

322.9 

645.9 

969 

1,292 

1,615 

,938 

2,261 

2,584 

2,906 

15.0 

132 

31 

324.  5 

649.0 

973 

1,298 

1,622 

,947 

2,  271 

2,596 

2,920 

15.2 

137 

32 

326.0 

652.  0 

978 

1,304 

1,630 

,956 

2,  282 

2,  608 

2,934 

15.4 

141 

33 

327.6 

655.1 

983 

1,310 

1  ,  63* 

,965 

2,  293 

2,621 

2,948 

15.6 

144 

34 

329.1 

658.  2 

987 

1,316 

1,646 

,975 

2,  304 

2,633 

2,  962 

15.  8   148 

35 

330.6 

661.3 

992 

1,323 

1,653 

,984 

2,  315 

2,645 

2,976 

16.0 

151 

36 

332.  2 

664.4 

997 

1,329 

1,661 

1,993 

2,  325 

2,658 

2,990 

16.2 

153 

37 

333.7 

667.5 

1,001 

1,335 

1,669 

2,  002 

2,336 

2,670 

3,004 

16.4  ;  159 

38 

335.3 

670.  5 

1,006 

1,341 

1,676 

2,012 

2,347 

2,682 

3,017 

16.6 

163 

39 

336.8 

673.6 

1,010 

1,347 

1  ,  684 

2,  021 

2,358 

2,695 

3,031 

16.8 

167 

40 

338.4 

676.7 

1,015 

1,  353 

1,692 

2,030 

2,369 

2,707 

3,045 

17.0 

170 

41 

339.9 

679.8 

1,020 

1,360 

1,700 

2,  039 

2,379 

2,719 

3,059 

17.2 

174 

42 

341.4 

682.  9 

1,024 

1,366 

1,707 

2,049 

2,390 

2,  732 

3,073 

17.4 

178 

43 

343.0 

686.0 

1,029 

1,372 

1,715 

2,  058 

2,  401 

2,744 

3,087 

17.6 

182 

44 

344.5 

689.1 

1,034 

1,378 

1,723 

2,  067 

2,412 

2,756 

3,101 

17.8 

186 

45 

346.1 

692.1 

1,038 

1,384 

1,730 

2,  076 

2,422 

2,  769 

3,115 

18.0 

190 

46 

347.6 

695.2 

1,043 

1,390 

1,738 

2,  086 

2,  433 

2,781 

3,  129 

18.2 

195 

47 

349.2 

698.3 

1,047 

1,397 

1,746 

2,095 

2,444 

2,793 

3,142 

18.4 

199 

48 

350.7 

701.4 

,052 

1,403 

1,753 

2,104 

2,  455 

2,806 

3,156 

18.6 

203 

49 

352.  2 

704.5 

,057 

1,409 

1,761 

2,113 

2,466 

2,818 

3,170 

18.8 

207 

50 

353.8 

707.6 

,061 

1,415 

1,769 

2,123 

2,476 

2,830 

3,184 

19.0 

212 

51 

355.3 

710.7 

,066 

1,421 

1,777 

2,  132 

2,487 

2,843 

3,198 

19.2 

216 

52 

356.9 

713.7 

,071 

1,427 

1,784 

2,  141 

2,498 

2,855 

3,  212 

19.4 

221 

53 

358.4 

716.8 

,075 

1,434 

1,792 

2,150 

2,509 

2,  867 

3,226 

19.6 

225 

54 

360.0 

719.9 

1,080 

1,440 

1,800 

2,160 

2,  520 

2,880 

3,240 

19.8 

230 

55 

361.5 

723.  0 

1,  085 

1,446 

1,807 

2,169 

2,530 

2,  892 

3,  253 

20.0 

234 

56 

363.0 

726.  1 

1,089 

1,452 

1,815 

2,178 

2,  541 

2,904 

3,267 

21.0 

258 

57 

364.6 

729.2 

1,094 

1,458 

1,823 

2,  188 

2,  552 

2,  917 

3,281 

22.0 

282 

58 

366.1 

732.3 

1,098 

1,465 

1,831 

2,197 

2,563 

2,929 

3,295 

23.0 

308 

59 

367.7 

735.3 

1,103 

1,471 

1,838 

2,  206 

2,574 

2,941 

3,309 

24.0 

335 

60 

369.2 

738.4 

1,108 

1,477 

1,846 

2,215 

2,584 

2,954 

3,323 

25.0 

363 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGEAPHIC    TABLES    AND    FORMULAS. 


279 


TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc.  —Continued. 


Corrections  for   curva- 

ture, refraction,   and 
height  of  instrument." 

0 

369.2 

738 

1,108 

1,477 

1,846 

2,215 

2,584 

2,954 

3,323 

1 

370.8 

742 

1,112 

1,483 

1,854 

2,225 

2,595 

2,966 

3,337 

Miles. 

Feet. 

Miles 

Feet. 

2 

372.3 

745 

1,117 

1,489 

1,862 

2,234 

2,606 

2,978 

3,351 

1.6 

6 

10.2 

64 

3 

373.8 

748 

1,122 

1,495 

1,869 

2,243 

2,617 

2,991 

3,  365 

2.1 

7 

10.3 

65 

4 

375.4 

751 

1,126 

1,502 

1,877 

2,  252 

2,628 

3,003 

3,378 

2.5 

8 

10.4 

67 

5 

376.9 

754 

1,131 

1,508 

1,885 

2,262 

2,639 

3,015 

3,392 

2.8 

9 

10.5 

68 

6 

378.5 

757 

1,135 

1,514 

1,892 

2,271 

2,649 

3,  028 

3,406 

3.1 

10 

10.6 

69 

7 

380.0 

760 

1,140 

1,520 

1,900 

2,280 

2,660 

3,040 

3,420 

3.4 

11 

10.7 

70 

8 

381.6 

763 

1,145 

1,526 

1,908 

2,289 

2,671 

3,053 

3,434 

3.6 

12 

10.8 

71 

9 

383.1 

766 

1,149 

1,532     1,916 

2,299 

2,682 

3,065 

3,448 

3.8 

13 

10.9 

73 

10 

384.7 

769 

1,154 

1,539 

1,923 

2,308 

2,  693 

3,077 

3,462 

4.1 

14 

11.0 

74 

11 

386.2 

772 

1,159 

1,545 

1,931 

2,317 

2,703 

3,090 

3,476 

4.3 

15 

11.1 

75 

12 

387.7 

775 

1,163 

1,551 

1,939 

2,326 

2,714 

3,102 

3,490 

4.5 

16 

11.2 

77 

13 

389.3 

779 

1,168 

1,557 

1,946 

2,336 

2,725 

3,114 

3,504 

4.7 

17 

11.3 

78 

14 

390.8 

782 

1,172 

1,563 

1,954 

2,345 

2,736 

3,127 

3,517 

4.8 

18 

11.4 

79 

15 

392.4 

785 

1,177 

1,569 

1,962 

2,354 

2,747 

3,139 

3,531 

5.0 

19 

11.5 

80 

16 

393.9 

788 

1,182 

1,576 

1,970 

2,363 

2,757 

3,151 

3,545 

5.2 

20 

11.6 

82 

17 

395.5 

791 

1,186 

1,582 

1,977 

2,373 

2,768 

3,164 

3,  559 

5.4 

21 

11.7 

83 

18 

397.0 

794 

1,191 

1,588 

1,985 

2,382 

2,779 

3,176 

3,573 

5.5 

22 

11.8 

84 

19 

398.6 

797 

1,196 

1,594 

1,993 

2,391 

2,790 

3,188 

3,587 

5.7 

23 

11.9 

86 

20 

400.1 

800     1,200 

1,600 

2,000 

2,401 

2,801 

3,201 

3,601 

5.8 

24 

12.0 

87 

21       401.6 

S03     1,205 

1,607 

2,008 

2,  410 

2,811 

3,213 

3,615 

6.0 

25 

12.1 

89 

22       403.2 

806     1,210     1,613 

2,016 

2,419 

2,822 

3,225 

3,629 

6.1 

26 

12.2 

90 

23       404.  7 

809     1,214     1,619 

2,024 

2,  428 

2,  833 

3,238 

3,643 

6.3 

27 

12.3 

91 

24       406.  3 

813     1,219     1,625 

2,031 

2,438 

2,844 

3,250 

3,656 

6.4 

28 

12.4 

93 

•J.~>       407.  8 

816     1,223     1,631 

2,039 

2,447 

2,855 

3,263 

3,  670 

6.5 

29 

12.5 

94 

20 

409.4 

819     1,228     1,637 

2,047 

2,456 

2,866 

3,275 

3,684 

6.7 

30 

12.6 

96 

27 

410.9 

822 

1,233  :  1,644 

2,055 

2,465 

2,876 

3,287 

3,698 

6.8 

31 

12.7 

97 

28 

412.5 

825 

1,237     1,650 

2,062 

2,475 

2,887 

3,300 

3,712 

6.9 

32 

12.8 

99 

29 

414.0 

828 

1,242 

1,656 

2,070 

2,484 

2,898 

3,312 

3,726 

7.0 

33 

12.9 

100 

30 

415.5 

831 

1,247 

1,662 

2,078 

2,493 

2,909 

3,324 

3,740 

7.2 

34 

13.0 

102 

31       417.1 

834 

1,251     1,668 

2,085 

2,503 

2,920 

3,337 

3,754 

7.3 

35 

13.1 

103 

32       418.  6 

837 

1,256  \  1,675 

2,093 

2,512 

2,930 

3,349 

3,768 

7.4 

36 

13.2 

105 

33       420.  2 

840 

1,261 

1,681 

2,101 

2,521 

2,941 

3,361 

3,782 

7.5 

37 

13.3 

106 

:«      421.7 

843 

1,265 

1,687 

2,109 

2,  530 

2,  952 

3,374 

3,796 

7.6 

38 

13.4 

108 

35       423.  3 

847 

1,270 

1,693 

2,116 

2,540 

2,963 

3,386 

3,809 

7.8 

39 

13.5 

109 

36       424.  8 

850 

1,274 

1,699 

2,124 

2,549 

2,974 

3,399 

3,823 

7.9 

40 

13.6 

111 

::7       426.4 

853 

1,279 

1,705 

2,132 

2,558 

2,985 

3,411 

3,837 

8.0 

41 

13.7 

112 

38       427.  9 

856 

1,284 

1,712 

2,140 

2,567 

2,995 

3,  423 

3,851 

8.1 

42 

13.8 

114 

39 

429.5 

859 

1,288 

1,718 

2,147 

2,577 

3,006 

3,436 

3,865 

8.2 

43 

13.9 

115 

40 

431.0 

862 

1,293 

1,724 

2,155 

2.586 

3,017 

3,448 

3,879 

8.3 

44 

14.0 

117 

t: 

432.5 

865 

1,298 

1,730 

2,163 

2,595 

3,028 

3,460 

3.S93 

8.4 

45 

14.1 

119 

4'2       434.  1  ' 

868 

1,302 

1,736 

2,  170 

2,  605 

3,039 

3,473 

3,907 

8.5 

46 

14.2 

120 

43       435.  6 

871 

1,307 

1,743 

2,178 

2,  614 

3,049 

3,  485 

3,921 

8.6 

47 

14.3 

122 

44       437.  2 

874 

1,312 

1,749 

2,186 

2,623 

3,060 

3,498 

3,  935 

8.7 

48 

14.4 

124 

45       438.  7 

877 

1,316 

1,755 

2,194 

2,632 

3,071 

3,510 

3,949 

8.8 

49 

14.5 

125 

46       440.  3 

881 

1,321 

1,761 

2,201 

2,642 

3,082 

3,522 

3,963 

8.9 

50 

14.6 

127 

47       441.8 

884 

1,325 

1,767 

2,209 

2,651 

3,093 

3,535 

3,976 

9.0 

51 

14.7 

129 

48       443.  4 

887 

1,330 

1,773 

2,217 

2,660 

3,104 

3,547 

3,990 

9.1 

52 

14.8 

130 

491   444.9 

890 

1,335 

1,780 

2,225 

2,669 

3,113 

3,558 

4,003 

9.2 

53 

14.9 

132 

50       446.5 

893 

1,339 

1,786 

2,232 

2,679 

3,125 

3,572 

4,018 

9.3 

54 

15.0 

134 

51       448.0 

896 

1,344 

1,792 

2,  240 

2,688 

3,136 

3,584 

4,032 

9.4 

55 

15.1 

135 

52       449.  6 

899 

1,349 

1,798 

2,248 

2,697 

3,147 

3,596 

4,046 

9.5 

56 

15.2 

137 

68       451.1 

902 

1,353 

1,804 

2,256 

2,707 

3,158 

3,609 

4,060 

9.6 

58 

15.3 

139 

54       452.  7 

905 

1,358 

1,811 

2,  263 

2,716 

3,169 

3,621 

4,074 

9.7 

59 

15.4 

141 

55       454.2 

908 

1,363 

1,817 

2,271 

2,  725 

3,179 

3,634 

4,088 

9.8 

60 

15.5 

142 

56       455.8 

912 

1,367 

1,823 

2,279 

2,735 

3,190 

3,646 

4,102 

9.9 

61 

15.6 

144 

57       457.  3 

915 

1,372 

1,829 

2,286 

2,744 

3,201 

3,658 

4,116 

10.0 

62 

15.7 

146 

58  i    458.8 

918 

1,377 

1/835 

2,294 

2,753 

3,212 

3,671 

4,130 

10.1 

63 

15.8 

148 

69      460.4 

921 

1,381 

1,842 

2,  302 

2,762 

3,223 

3,683 

4,144 

15.9 

150 

16.0 

151 

60 

461.9 

924 

1,386 

1,848 

2,310 

2,772 

3,234 

3,6% 

4,157 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  6  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


280  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

5° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections   for  curva- 
ture,  refraction,   and 
height  of  instrument.a 

0 

461.9 

924 

1,386 

1,848 

2,310 

2,772 

3,234 

3,696 

4,157 

1 

463.5 

927 

1,390 

1,854 

2,317 

2,781 

3,244 

3,  708 

4,171 

Miles. 

Feet. 

Miles: 

Feet. 

2 

465.0 

930 

1,395 

1,860 

2,325 

2,790 

3,255 

3,720 

4,185 

1.6 

6 

10.2 

64 

3 

466.6 

933 

1,400 

1,866 

2,333 

2,800 

3,266 

3,733 

4,199 

2.1 

7 

10.3 

65 

4 

468.1 

936 

1,405 

1,873 

2,341 

2,809 

3,277 

3,745 

4,213 

2.5 

8 

10.4 

67 

5 

469.7 

939 

1,409 

1,879 

2,348 

2,818 

3,288 

3,757 

4,227 

2.8 

9 

10.5 

68 

6 

471.2 

942 

1,414 

1,885 

2,356 

2,827 

3,299 

3,770 

4,241 

3.1 

10 

10.6 

69 

7 

472.8 

946 

1,419 

1,891 

2,364 

2,837 

3,309 

3,  782 

4,255 

3.4 

11 

10.7 

70 

8 

474.3 

949 

1,423 

1,897 

2,372 

2,  846 

3,320 

3,  795 

4,269 

3.6 

12 

10.8 

71 

9 

475.9 

952 

1,428 

1,904 

2,379 

2,855 

3,331 

3,807 

4,283 

3.8 

13 

10.9 

73 

10 

477.4 

955 

1,432 

1,910 

2,387 

2,865 

3,342 

3,  819 

4,297 

4.1 

14 

11.0 

74 

11 

479.0 

958 

1,437 

1,916 

2,395 

2,874 

3,353 

3,832 

4,311 

4.3 

15 

11.1 

75 

12 

480.5 

961 

1,442 

1,922 

2,403 

2,883 

3,  364 

3,844 

4,325 

4.5 

16 

11.2 

77 

13 

482.1 

964 

1,447 

1,928 

2,410 

2,892 

3,375 

3,857 

4,339 

4.7 

17 

11.3 

78 

-14 

483.6 

967 

1,451 

1,935 

2,418 

2,  902 

3,385 

3,869 

4,353 

4.8 

18 

11.4 

79 

15 

485.2 

970 

1,456 

1,941 

2,426 

2,911 

3,396 

3,881 

4,367 

5.0 

19 

11.5 

80 

16 

486.7 

973 

1,461 

1,947 

2,434 

2,  920 

3,407 

3,894 

4,381 

5.2 

20 

11.6 

82 

17 

488.3 

976 

1,465 

1,953 

2,441 

2,930 

3,418 

3,906 

4,394 

5.4 

21 

11.7 

83 

18 

489.8 

980 

1,470 

1,959 

2,449 

2,939 

3,  429 

3,919 

4,408 

5.5 

22 

11.8 

84 

19 

491.3 

983 

1,475 

1,966 

2,457 

2,948 

3,440 

3,931 

4,422 

5.7 

23 

11.9 

86 

20 

492.9 

986 

1,479 

1,972 

2,465 

2,958 

3,450 

3,943 

,436 

5.8 

24 

12.0 

87 

21 

494.5 

989 

1,483 

1,978 

2,  472 

2,967 

3,461 

3,  956 

,450 

6.0 

25 

12.1 

89 

22 

496.0 

992 

1,488 

1,984 

2,  480 

2,976 

3,  472 

3,968 

,464 

6.1 

26 

12.2 

90 

23 

497.6 

995 

1,493 

1,990 

2,488 

2,985 

3,483 

3,981 

,478 

6.3 

27 

12.3 

91 

24 

499.1 

998 

1,498 

1,996 

2,496 

2,995 

3,  494 

3,993 

,492 

6.4 

28 

12.4 

93 

25 

500.  7 

,001 

1,502 

2,003 

2,503 

3,004 

3,  505 

4,005 

,506 

6.5 

29 

12.5 

94 

26 

502.2 

,004 

1,507 

2,009 

2,  511 

3,013 

3,515 

4,018 

,520 

6.7 

30 

12.6 

96 

27 

503.8 

,007 

1,512 

2,015 

2,519 

3,023 

3,  526 

4,030 

4,534 

6.8 

31 

12.7 

97 

28 

505.3 

,010 

1,516 

2,021 

2,527 

3,  032 

3,537 

4,042 

4,548 

6.9 

32 

12.8 

99 

29 

506.9 

,014 

1,521 

2,027 

2,534 

3,041 

3,548 

4,055 

4,562 

7.0 

33 

12.9 

100 

30 

508.4 

,017 

1,525 

2,034 

2,542 

3,050 

3,559 

4,067 

4,576 

7.2 

34 

13.0 

102 

31 

510.0 

,020 

1,530 

2,040 

2,  550 

3,060 

3,570 

4,080 

4,590 

7.3 

35 

13.1 

103 

32 

511.5 

,023 

1,535 

2,046 

2,558 

3,069 

3,581 

4,  092 

4,604 

7.4 

36 

13.2 

105 

33 

513.0 

,026 

1,539 

2,052 

2,565 

3,078 

3,591 

4,105 

4,618 

7.5 

37 

13.3 

106 

34 

514.6 

,029 

1,544 

2,  058 

2,573 

3,088 

3,602 

4,117 

4,  632 

7.6 

38 

13.4 

108 

35 

516.2 

,032 

1,549 

2,065 

2,581 

3,097 

3,613 

4,129 

4,645 

7.8 

39 

13.5 

109 

36 

517.7 

,035 

1,553 

2,071 

2,  589 

3,106 

3,  624 

4,142 

4,659 

7.9 

40 

13.6 

111 

37 

519.3 

,039 

1,558 

2,077 

2,596 

3,116 

3,635 

4,154 

4,673 

8.0 

41 

13.7 

112 

38 

520.8 

,042 

1,563 

2,083 

2,604 

3,125 

3,646 

4,167 

4,687 

8.1 

42 

13.8 

114 

39 

522.  4 

,045 

1,568 

2,089 

2,612 

3,134 

3,657 

4,179 

4,701 

8.2 

43 

13.9 

115. 

40 

523.9 

,048 

1,572 

2,095 

2,620 

3,144 

3,667 

4,191 

4,715 

8.3 

44 

14.0 

117 

41 

525.5 

,051 

1,576 

2,  102 

2,  627 

3,153 

3,678 

4,  204 

4,729 

8.4 

45 

14.1 

i*e 

42 

527.0 

,054 

1,581 

2,108 

2,635 

3,  162 

3,689 

4,  216 

4,  743 

8.5 

46 

'14.2 

120 

43 

528.6 

,057 

1,586 

2,114 

2,643 

3,172 

3,700 

4,229 

4,757 

8.6 

47 

14.3 

122 

44 

530.1 

,060 

1,591 

2,121 

2,651 

3,181 

3,711 

4,241 

4,771 

8.7 

48 

14.4 

124 

45 

531.7 

,063 

1,595 

2,127 

2,658 

3,190 

3,  722 

4,253 

4,785 

8.8 

49 

14.5 

125 

46 

533.2 

,066 

1,600 

2,133 

2,666 

3,199 

3,733 

4,  266 

4,799 

8.9 

50 

14.6 

127 

47 

534.8 

,070 

1,605 

2,139 

2,674 

3,209 

3,743 

4,278 

4,813 

9.0 

51 

14.7 

129 

48 

536.3 

,073 

1,609 

2,145 

2,  682 

3,218 

3,754 

4,291 

4,827 

9.1 

52 

14.8 

130 

49 

537.9 

,076 

1,614 

2,154 

2,689 

3,227 

3,765 

4,303 

4,841 

9.2 

53 

14.9 

132 

50 

539.4 

,079 

1,618 

2,158 

2,697 

3,237 

3,776 

4,315 

4,855 

9.3 

54 

15.0 

134 

51 

541.0 

,082 

1,623 

2,  166 

2,705 

3,246 

3,787 

4,  32S 

4,869 

9.4 

55 

15.1 

135 

52 

542.5 

,085 

1,628 

2,170 

2,713 

3,255 

3,798 

4,340 

4,883 

9.5 

56 

15.2 

137 

53 

544.  1 

,088 

1,632 

2,176 

2,721 

3,265 

3,809 

4,353 

4,897 

9.6 

58 

15.3 

139 

54 

545.6 

,091 

1,637 

2,183 

2,728 

3,274 

3,819 

4,365 

4,911 

9.7 

59 

15.4 

141 

55 

547.2 

,094 

1,642 

2,189 

2,736 

3,283 

3,830 

4,378 

4,925 

9.8 

60 

15.5 

142 

56 

548.7 

,097 

1,646 

2,195 

2,743 

3,292 

3,841 

4,390 

4,939 

9.9 

61 

15.6 

144 

57 

550.3 

1,101 

1,651 

2,201 

2,752 

3,  302 

3,852 

4,  402 

4,953 

10.0 

62 

15.7 

146 

58 

551.8 

1,104 

1,656 

2,207 

2,759 

3,311 

3,863 

4,  415 

4,967 

10.1 

63 

15.8 

148 

59 

553.4 

1,107 

1,661 

2,214 

2,  76.7 

3,320 

3,874 

4,427 

4,981 

15.9 

150 

16.0 

151 

60 

555.  0 

1,110 

1,665 

2,220 

2,775 

3,330 

3,885 

4,440 

4,995 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGRAPHIC  TABLES  AND  FORMULAS.          281 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

6° 


1 

2 

3 

4 

5 

6 

1 

8 

9 

Corrections  for  curva- 
ture, refraction  and 
height  of  instrument.** 

0 

555.0 

1,110 

1,665 

2,220 

2,775 

3,330 

3,885 

4,440 

4,995 

1 

556.5 

1,113 

1,670 

2,226 

2,783 

3,339 

3,896 

4,452 

5  009 

Miles 

Feet. 

Miles. 

Feet. 

2 

558.1 

1,116 

1,674 

2,  232 

2,790 

3,348 

3,906 

4,464 

5,023 

1.6 

6 

10.2 

64 

3 

559.6 

1,119 

1,679 

2,238 

2,  798 

3,358 

3,917 

4,477 

5,037 

2.1 

7 

10.3 

65 

4 

561.2 

1,122 

1,684 

2,  245 

2,806 

3,367 

3,  928 

4,  489 

5,050 

2.5 

8 

10.4 

67 

5 

562.7 

1,125 

1,688 

2,251 

2,814 

3,376 

3,939 

4,  502 

5,064 

2.8 

9 

10.5 

68 

6 

564.3 

1,129 

1,693 

2,  257 

2,821 

3,386 

3,950 

4,514 

5,078 

3.1 

10 

10.6 

69 

7 

565.8 

1,132 

1,697 

•2,  263 

2,829 

3,395 

3,961 

4,527 

5,  092 

3.4 

11 

10.7 

70 

8 

567.4 

1,135 

1,702 

2,  270 

2,  837 

3,404 

3,  972 

4,539 

5,106 

3.6 

12 

10.8 

71 

9 

568.9 

1,138 

1,707 

2,  276 

2,845 

3,414 

3,  983 

4,551 

5,120 

3.8 

13 

10.9    73 

10 

570.5 

1,141 

1,711 

2,  282 

2,852 

3,423 

3,993 

4,564 

5,  134 

4.1 

14 

11.0    74 

11 

572.0 

1,144 

1,716 

2,288 

2,860 

3,  432 

4,004 

4,576 

5,148 

4.3 

15 

11.1    75 

12 

573.6 

1,147 

1,721 

2,294 

2,868 

3,442 

4,015 

4,589 

5,162 

4.5 

16 

11.  2    77 

13 

575.2 

1,150 

1,725 

2,301 

2,876 

3,451 

4,026 

4,601 

5,176 

4.7 

17 

11.3    78 

14 

576.7 

1,153 

1,730 

2,307 

2,884 

3,460 

4,037 

4,614 

5,190 

4.8 

18 

11.4 

79 

15 

578.3 

1,157 

1,7135 

2,313 

2,  891 

3,470 

4,048 

4,626 

5,204 

5.0 

19 

11.5 

80 

16 

579.8 

1,160 

1,739 

2,319 

2,899 

3,479 

4,059 

4,639 

5,218 

5.2 

20 

11.6 

82 

17 

581.4 

1,163 

1,744 

2,325 

2,907 

3,488 

4,070 

4,651 

5,232 

5.4 

21 

11.7 

83 

18 

582.9 

1,166 

1,749 

2,332 

2,915 

3,498 

4,080 

4,663 

5,246 

5.5 

22 

11.8 

84 

19 

584.5 

1,169 

1,753 

2,338 

2,922 

3,507 

4,  091 

4,676 

5,260 

5.7 

23 

11.9 

86  ! 

20 

586.0 

1,172 

1,758 

2,344 

2,930 

3,516 

4,102 

4,688 

5,274 

5.8 

24 

12.0 

87 

21 

587.6 

1,175 

1,763 

2,350 

2,938 

3,526 

4,113 

4,701 

5,288 

6.0 

25 

12.1 

89 

22 

589.1 

1,178 

1,767 

2,357 

2,946 

3,  535 

4,124 

4,713 

5,302 

6.1 

26 

12.2 

90 

23 

590.7 

1,181 

1,772 

2,363 

2,  953 

3,544 

4,135 

4,726 

5,  316 

6.3 

27 

12.3 

91 

•J! 

592.2 

1,185 

1,777 

2,369 

2,961 

3,554 

4,146 

4,738 

5,330 

6.4 

28 

12.4 

93 

25 

593.8 

1,188 

1,781 

2,375 

2,969 

3,563 

4,157 

4,750 

5,344 

6.5 

29 

12.5 

94 

26 

595.4 

1,191 

1,786 

2,381 

2,977 

3,572 

4,168 

4,763 

5,358 

6.7 

30. 

12.6 

96 

27 

596.9 

1,194 

1,791 

2,388 

2,985 

3,581 

4,178 

4,775 

5,  372 

6.8 

31 

12.7 

97 

28 

598.  5 

1,197 

1,795 

2,394 

2,992 

3,591 

4,189 

4,788 

5,386 

6.9 

32 

12.8 

99 

29 

600.0 

1,200 

1,800 

2,400 

3,000 

3,600 

4,200 

4,800 

5,400 

7.0 

33 

12.9 

100 

30 

601.6 

1,203 

1,805 

2,406 

3,008 

3,609 

4,211 

4,813 

5,  414 

7.2 

34 

13.0 

102 

31 

603.1 

1,206 

1,809 

2,413 

3,016 

3,619 

4,222 

4,825 

5,428 

7.3 

35 

13.1 

103 

32 

604.7 

1,209 

1,814 

2,419 

3,023 

3,  628 

4,233 

4,838 

5,  442 

7.4 

36 

13.2 

105 

33 

606.3 

1,213 

1,819 

2,  425 

3,031 

3,637 

4,244 

4,850 

5,  456 

7.5 

37 

13.3 

106 

34 

607.8 

1,216 

1,823 

2,431 

3,039 

3,647 

1,255 

4,862 

5,470 

7.6 

38 

13.4 

108 

35 

609.4 

1,219 

1,828 

2,437 

3,047 

3,656 

4,  266 

4,875 

5,484 

7.8 

39 

13.5 

109 

36  !  610.9 

1,222 

1,833 

2,444 

3,  055 

3,666 

4,276 

4,887 

5,498 

7.9 

40 

13.6 

111 

37   612.  5 

1,225 

1,837 

2,450 

3,062 

3,675 

4,287 

4,900 

5,512 

8.0 

41 

13.7 

112 

38   614.  0 

1,228 

J.8-I2 

2,456 

3,070 

3,684 

4,298 

4,912 

5,526 

8.1 

42 

13.8 

114 

39   615.  5 

1,231 

1,847 

2,462 

3,078 

3,694 

4,309 

4,925 

5,540 

8.2 

43 

13.9 

115 

40 

617.2 

1,234 

1,851 

2,469 

3,086 

3,703 

4,320 

4,937 

5,554 

8.3 

44 

14.0 

117 

41 

618.7 

1,237 

1,856 

2,475 

3,094 

3,712 

4,  331 

4,950 

5,568 

8.4 

46 

14.1 

119 

42 

620.3 

1,241 

1,861 

2,481 

3,101 

3,722 

4,342 

4,  962 

5,582 

8.5 

46 

14.2 

120 

43 

621.8 

1,244 

1,865 

2,487 

3,109 

3,731 

4,353 

4,975 

5,596 

8.6 

47 

14.3 

122 

44 

623.4 

1,247 

1,870 

2,494 

3,117 

3,740 

4,364 

4,987 

5,  610 

8.7 

48 

14.4 

124 

45 

624.9 

1,250 

1,875 

2,500 

3,  125 

3,750 

4,374 

4,999 

5,  624 

8.8 

49 

14.5 

125 

46 

626.5 

1,253 

1,879 

2,506 

3,132 

3,759 

4,  385 

5,  012 

5,638 

8.9 

50 

14.6 

127 

47 

628.0 

1,256 

1,884 

2,  512 

3,140 

3,768 

4,396 

5,  024 

5,653 

9.0 

51 

14.7 

129 

48 

629.6 

1,259 

1,889 

2,518 

3,148 

3,778 

4,407 

5,037 

5,667 

9.1 

52 

14.8 

130 

49 

631.2 

1,262 

1,894 

2,  525 

3,156 

3,787 

4,418 

5,049 

5,681 

9.2 

53 

14.9 

132 

50 

632.7 

1,265 

1,898 

2,  531 

3,164 

3,796 

4,429 

5,062 

5,695 

9.3 

54 

15.0 

134 

51 

634.3  1 

1,269 

1,903 

2,  537 

3,171 

3,806 

4,440 

5,074 

5,709 

9.4 

55 

15.  1 

135 

52 

635.8 

1,272 

1,908 

2,543 

3,179 

3,815 

4,451 

5,087 

5,723 

9.5 

56 

15.2 

137 

53 

637.4 

1,275 

1,912 

2,550 

3,187 

3,824 

4,462 

5,099 

5,737 

9.6 

58 

15.3 

139 

54 

638.9 

1,278 

1,917 

2,  556 

3,  195 

3,834 

4,473 

5,112 

5,751 

9.7 

59 

15.4 

141 

55 

640.5 

1,281 

1,922 

2,562 

3,203 

3,843 

4,484 

5,124 

5.765 

9.8 

60 

15.5 

142 

M 

642.1 

1,284 

1,926 

2,568 

3,210 

3,852 

4,494 

5,  136 

5,779 

9.9 

61 

15.6 

144 

57 

643.6 

1,287 

1,931 

2,  575 

3,218 

3,862 

4,505 

5,149 

5,793 

10.0 

62 

15.7 

146 

58 

645.  2 

1,290 

1,936 

2,581 

3,226 

3,871 

4,516 

5,161 

5,  807 

10.1 

63 

15.8 

148 

59 

646.7 

1,293 

1,940 

2,587 

3,234 

3,880 

4,  527 

5,174 

5,821 

15.9 

150 

16.0 

151 

60 

648.3 

1,297 

1,  945 

2,  59o 

3,242 

3,890 

4,538 

5,186 

5,835 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.6  feet. 


282  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

7° 


1 

2 

3 

4 

0 

6 

7 

8 

9 

Corrections   for  curva- 
ture,  refraction    and 
height  of  instrument.a 

0 

648.3 

1,297 

1,945 

2,  593 

3,242 

3,890 

4,538 

5,186 

5,835 

1 

649.9 

1,300 

1,950 

2,599 

3,249 

3,899 

4,549 

5,199 

5,849 

Miles. 

Feet. 

Miles. 

Feet. 

2 

651.4 

,303 

1,954 

2,606 

3,257 

3,909 

4,560 

5,211 

5,  863 

1.6 

6 

10.2 

64 

3 

653.0 

,306 

1,959 

2,  612 

3,265 

3,918 

4,571 

5,  224 

5,  877 

2.1 

7 

10.3 

65 

4 

654.5 

,309 

1,964 

2,618 

3,273 

3,  927 

4,582 

5,236 

5,891 

2.5 

8 

10.4 

67 

5 

656.1 

,312 

1,968 

2,624 

3,281 

3,937 

4,593 

5,  249 

5,905 

2.8 

9 

10.5 

68 

6 

657.7 

,315 

1,973 

2,631 

3,288 

3,946 

4,604 

5,  261 

5,919 

3.1 

10 

10.6 

69 

7 

659.  2 

,318 

1,978 

2,637 

3,296 

3,  955 

4,615 

5,274 

5,  933 

3.4 

11 

10.7 

70 

8 

660.8 

1,322 

1,982 

2,  643 

3,304 

3,965 

4,626 

5,286 

5,  947 

3.6 

12 

10.8 

71 

9 

662.4 

1,325 

1,987 

2,649 

3,312 

3,974 

4,636 

5,  299 

5,961 

3.8 

13 

10.9 

73 

10 

663.9 

1,328 

1,992 

2,656 

3,320 

3,983 

4,647 

5,311 

5,975 

4.1 

14 

11.0 

74 

11 

665.5 

1,331 

1,996 

2,662 

3,  327 

3,993 

4,658 

5,  324 

5,  989 

4.3 

15 

11.1 

75 

12 

667.0 

1.334 

2,001 

2,668 

3,335 

4,002 

4,669 

5,336 

6,003 

4.5 

16 

11.2 

77 

13 

668.6 

1,337 

2,006 

2,  674 

3,  343 

4,012 

4,680 

5,349 

6,017 

4.7 

17 

11.3 

78 

14 

670.2 

1,340 

2,  010 

2,681 

3,351 

4,021 

4,691 

5,361 

6,031 

4.8 

18 

11.4 

79 

15 

671.7 

1,343 

2,015 

2,687 

3,  359 

4,030 

4,  702 

5,374 

6,045 

5.0 

19 

11.5 

80 

16 

673.3 

1,347 

2,020 

2,693 

3,366 

4,040 

4,713 

5,386 

6,060 

5.2 

20 

11.6 

82 

17 

674.8 

1,350 

2,025 

2,699 

3,374 

4,049 

4,724 

5,399 

6,074 

'   5.4 

21 

11.7 

83 

18 

676.4 

J,353 

2,029 

2,706 

3,382 

4,058 

4,735 

5,411 

6,088 

5.5 

22 

11.8 

84 

19 

678.0 

1,356 

2,034 

2,712 

3,390 

4,068 

4,746 

5,424 

6,102 

5.7 

23 

11.9 

86 

20 

679.5 

1,359 

2,039 

2,718 

3,398 

,077 

4,757 

5,436 

6,116 

5.8 

24 

12.0 

87 

21 

681.1 

1,362 

2,043 

2,724 

3,  405 

,087 

4,768 

5,  449 

6,130 

6.0 

25 

12.1 

89 

22 

682.6 

1,365 

2,048 

2,731 

3,413 

,096 

4,779 

5,461 

6,144 

6.1 

26 

12.2 

90 

23 

684.2 

1,  368 

2,053 

2,  737 

3,421 

,105 

4,789 

5,474 

6,158 

6.3 

27 

12.3 

91 

24 

685.8 

1,372 

2,  057 

2,743 

3,  429 

,115 

4,800 

5,486 

6,172 

6.4 

28 

12.4 

93 

25 

687.3 

1,375 

2,062 

2,  749 

3,437 

,124 

4,811 

5,499 

6,186 

6.5 

29 

12.5 

94 

26 

688.9 

1,378 

2,  067 

2,756 

3,444 

4,133 

4,822 

5,511 

6,  200 

6.7 

30 

12.6 

96 

27 

690.5 

1,381 

2,  071 

2,  762 

3,452 

4,143 

4,833 

5,  524 

6,214 

6.8 

31 

12.7 

97 

28 

692.0 

1,384 

2,076 

2,768 

3,460 

4,152 

4,844 

5,536 

6,228 

6.9 

32 

12.8 

99 

29 

693.  6 

1,387 

2,081 

2,774 

3,468 

4,161 

4,855 

5,549 

6,242 

7.0 

33 

12.9 

100 

30 

695.1 

1,390 

2,  085 

2,781 

3,476 

4,171 

4,866 

5,561 

6,  256 

7.2 

34 

13.0 

102 

31 

696.7 

1,393 

2,090 

2,787 

3,483 

4,180 

4,877 

5,  574 

6,  270 

7.3 

35 

13.1 

103 

32 

698.3 

,396 

2,  095 

2,793 

3,491 

4,190 

4,888 

5,  586 

6,  284 

7.4 

36 

13.2 

105 

33 

699.8 

,400 

2,099 

2,799 

3,  499 

4,199 

4,899 

5,  599 

6,298 

7.5 

37 

13.3 

106 

34 

701.4 

,403 

2,  104 

2,806 

3,507 

4,208 

4,910 

5,  611 

6,  312 

7.6 

38 

13.4 

108 

35 

702.9 

,406 

2,  109 

2,812 

3,515 

4,  218 

4,921 

5,624 

6,  327 

7.8 

39 

13.5 

109 

36 

704.5 

,409 

2,114 

2,818 

3,523 

4,  227 

4,932 

5,636 

6,341 

7.9 

40 

13.6 

111 

37 

706.1 

,412 

2,118 

2,824 

3,530 

4,236 

4,943 

5,649 

6,  355 

8.0 

41 

13.7 

112 

38 

707.6 

,415 

2,  123 

2,831 

3,538 

4,246 

4,953 

5,661 

6,369 

8.1 

42 

13.8 

114 

39 

709.2 

,418 

2,128 

2,837 

3,546 

4,255 

4,964 

5,674 

6,383 

8.2 

43 

13.9 

115 

40 

710.8 

,422 

2,  132 

2,843 

3,554 

4,265 

4,975 

5,686 

6,397 

8.3 

44 

14.0 

117 

41 

712.3 

,425 

2,137 

2,849 

3,562 

4,  274 

4,986 

5,699 

6,411 

8.4 

45 

14.1 

119 

42 

713.9 

,428 

2,142 

2,856 

3,569 

4,  283 

4,997 

5,711 

6,425 

8.5 

46 

14.2 

120 

43 

715.  5 

,431 

2,146 

2,862 

3,  577 

4,  293 

5,  008 

5,  724 

6,439 

8.6 

47 

14.3 

122 

44 

717.0 

,434 

2,  151 

2,868 

3,  585 

4,302 

5,019 

5,736 

6,453 

8.7 

48 

14.4 

124 

45 

718.6 

,437 

2,156 

2,  874 

3,593 

4,312 

5,030 

5,749 

6,467 

8.8 

49 

14.5 

125 

46 

720.  2 

,440 

2,160 

2,881 

3,601 

4,321 

5,041 

5,  761 

6,481 

8.9 

50 

14.6 

127 

47 

721.7 

,443 

2,  165 

2,887 

3,609 

4,330 

5,  052 

5,  774 

6,  495 

9.0 

51 

14.7 

129 

48 

723.3 

,447 

2,  170 

2,893 

3,616 

4,340 

5,063 

5,  786 

6,  510 

9.1 

52 

14.8 

130 

49 

724.8 

,  450     2,  175 

2,899 

3,624 

4,349 

5,  074 

5,799 

6,524 

9.2 

53 

14.9 

132 

50 

726.4 

,  453     2,  179 

2,906 

3,  632 

4,358 

5,085 

5,811 

6,538 

9.3 

54 

15.0 

134 

51 

728.0 

,  456     2,  184 

2,912 

3,640 

4,368 

5,  096 

5,824 

6,  552 

9.4 

55 

15.1 

135 

52 

729.5 

,  459     2,  189 

2,  918 

3,648 

4,377 

5,107 

5,836 

6,  566 

9.5 

56 

15.2 

137 

53 

731.1 

,  462     2,  193 

2,924 

3,656 

4,387 

5,118 

5,849 

6,580 

9.6 

58 

15.3 

139 

54 

732.7 

,  465     2,  198 

2,931 

3,663 

4,396 

5,  129 

5,861 

6,594 

9.7 

59 

15.4 

141 

55 

734.2 

,  468     2,  203 

2,037 

3,671 

4,  405 

5,  140 

5,874 

6,608 

9.8 

60 

15.5 

142 

56 

735.8 

,472 

2,207 

2,943 

3,679 

4,415 

5,151 

5,886 

6,622 

9.9 

61 

15.6 

144 

57 

737.4 

,475 

2,212 

2,949 

3,687 

4,424 

5,162 

5,899 

6,636 

10.0 

62 

15.7 

146 

58 

738.9 

,478 

2,217 

2,956 

3,695 

4,434 

5,172 

5,911 

6,650 

10.1 

63 

15.8 

148 

59 

740.5 

,481 

2,221 

2,962 

3,702 

4,443 

5,183 

5,924 

6,664 

15.9 

J50 

16.0 

151 

60 

742.1 

1,484 

2,226 

2,968 

,3,  710 

4,452 

5,  194 

5,936 

6,678 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  283 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc.—  Continued. 

8° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections   for  curva- 
ture, refraction,  and 
height  of  instruments 

0 

742.  1 

1,484 

2,226 

2,968 

3,710 

4,452 

5,194 

5,936 

6,678 

1 

743.6 

1,487 

2,  231 

2,  974 

3,  718 

4,462 

5,205 

5,949 

6,693 

Miles. 

Feet. 

Miles. 

Feet. 

2 

745.  2 

1,490 

'2,  236 

2,981 

3,  726 

4,471 

5,216 

5,962 

6,707 

1.6 

6 

10.2 

64 

3       746.8 

1,494 

2,  240 

2,  987 

3.734 

4,481 

5,227 

5,  974 

6,721 

2.1 

7 

10.3 

65 

4       748.  3 

1,497 

2,  245 

2,  993 

3,742 

4,490 

5,238 

5,987 

6,735 

2.5 

8 

10.4 

67 

5       749.  9 

1,500 

2,250 

3,000 

3,749 

4,499 

5,249 

5,999. 

6,749 

2.8 

9 

10.5 

68 

6       751.  5 

1,503 

2,254 

3,006 

3,757 

4,509 

5,260 

6,012 

6,763 

3.1 

10 

10,6 

69 

7       753.0 

1,506 

2,259 

3,  012 

3,765 

4,518 

5,271 

6,  024 

6,777 

3.4 

11 

10.7 

70 

8       754.6 

1,509 

2,  264 

3,018 

3,773 

4,528 

5,  282 

6,037 

6,791 

3.6 

12 

10.8 

71 

9       756.  2 

1,512 

2,269 

3,025 

3,781 

4,537 

5,293 

6,049     6;806 

3.8 

13 

10.9 

73 

10 

757.7 

1,515 

2,273 

3,031 

3,789 

4,546 

5,304 

6,062 

6,820 

4.1 

14 

11.0 

74 

11       759.  3 

1,519 

2,278 

3,037 

3,797 

4,556 

5,315 

6,074 

6,834 

4.3 

15 

11.1 

75 

12       760.  9 

1,522 

2,283 

3,043 

3,804 

4,565 

5,326 

6,087 

6,848 

4.5 

16 

11.2 

77 

13       762.4 

1,525 

2,287 

3,050 

3,812 

4,575 

5,337 

6,100 

6,862 

4.7 

17 

11.3 

78 

14       764.  0 

1,528 

2,  292 

3,056 

3,820 

4,584 

5,348 

6,  112 

6,876 

4.8 

18 

11.4 

79 

15       765.  6 

1,531 

2,  297 

3,  062 

3,828 

4,593 

5,359 

6,  125 

6,890 

5.0 

19 

11.5 

80 

16       767.  1 

1,534 

2,301 

3,069 

3,836 

4,603 

5,370 

6,137 

6,904 

5.2 

20 

11.6 

82 

17       768.  7 

1,537 

2,306 

3,075 

3,  844 

4,  612 

5,381 

6,150 

6,918 

5.4 

21 

11.7 

83 

18       770.3 

1,541 

2,311 

3,081 

3,851 

4,  622 

5,392 

6,162 

6,933 

5.5 

22 

11.8 

.    84 

19 

771.8 

1,544 

2,316 

3,087 

3,859 

4,  631 

5,403 

6,175 

6,947 

5.7 

23 

11.9 

86 

20 

773.4 

1,547 

2,  320 

3,094 

3,867 

4,640 

5,414 

6,187 

6,961 

5.8 

24 

12.0 

87 

21       775.0 

1,560 

2,325 

3,100 

3,  875 

4,650 

5,425 

6,200 

6,975 

6.0 

25 

12.1 

89 

22       776.  6 

1,563 

2,330     3,106 

3,883 

4,659 

5,436 

6,  212 

6,989 

6.1 

26 

12.2 

90 

23       778.  1 

1,556 

2,  334     3,  112 

3,891 

4,669 

5,447 

6,225 

7,003 

6.3 

27 

12.3 

91 

24        779.  7 

1,559 

2,339     3,119 

3,898 

4,678 

5,458 

6,  237 

7,017 

6.4 

28 

12.4 

93 

25       781.  3 

1,562 

2,344     3,125 

3,906 

4,688 

5,469 

6,  250 

7,031 

6.5 

29 

12.5 

94 

26       782.8 

1,566 

2,348     3,131 

3,914 

4,697 

5,480 

6,263 

7,045 

6.7 

30 

12.6 

96 

27       784.  4 

1,569 

2,353     3,138 

3,  922 

4,706 

5,491 

6,  275 

7,060 

6.8 

31 

12.7 

97 

28       786.0 

1,572 

2,  358     3,  144 

3,930 

4,716 

5,502 

6,288 

7,074 

6.9 

32 

12.8 

99 

29 

787.5 

1,575 

2,363 

3,150 

3,938 

4,  725 

5,513 

6,800 

7,088 

7.0 

33 

12.9 

100 

30 

789.1 

1,578 

2,367 

3,156 

3,945 

4,735 

5,524 

6,313 

7,  102 

7.2 

34 

13.0 

102 

Ml 

790.7 

1,581 

2,  372     3,  163 

3,953 

4,744 

5,535 

6,325 

7,116 

7.3 

35 

13.1 

103 

32 

792.2 

1,584 

2,377  !  3,169 

3,961 

4,753 

5,546 

6,338 

7,130 

7.4 

36 

13.2 

105 

33 

798.  8     1,  588 

2,381     3,175 

3,969 

4,763 

5,557 

6,  351 

7,144 

7.5 

37 

13.3 

106 

34 

795.4      1,  r>'.»l 

2,  386     3,  182 

3,977 

4,772 

5,568 

6,363 

7,159 

7.6 

38 

13.4 

108 

35       796.9     1,594 

2,391  i  3,188 

3,985 

4,782 

5,579 

6,376 

7,173 

7.8 

39 

13.5 

109 

36       798.5     1,597 

2,396  '  3,194 

3,993 

4,791 

5,590 

6,388 

7,187 

7.9 

40 

18.6 

111 

37       800.1      1,600 

2,400  i  3,200 

4,  001     4,  801 

5,601 

6,401 

7,201 

8.0 

41 

13.7 

112 

38       801.7 

1,603 

2,405 

3,  207 

4,008 

4,810 

5,612 

6,414 

7,215 

8.1 

42 

13.8 

114 

39       803.  2 

1,607 

2,410 

3,213 

4,016 

4,820 

5,623 

6,426 

7,229 

8.2 

43 

13.9 

115 

4u       804.8 

1,610 

2,414 

3,219 

4,024 

4,829 

5,634 

6,  439 

7,243 

8.3 

44 

14.0 

117 

41 

806.4 

1,613 

2,419 

3,226 

4,  032 

4,838 

5,  645 

6,451 

7,258 

8.4 

45 

14.1 

119 

42 

808.0 

1,616 

2,424 

3,  232 

4,040 

4,848 

5,656 

6,464 

7,  272 

8.5 

46 

14.2 

120 

43 

809.5 

1,619 

2,429 

3,238 

4,048 

4,857 

5,667 

6,476 

7,286 

8.6 

47 

14.3 

.122 

44 

811.1 

1,622 

2,433 

3,244 

4,056 

4,867 

5,678 

6,489 

7,300 

8.7 

48 

14.4 

124 

45 

812.7 

1,625 

2,  438 

3,251 

4,063 

4,876 

5,689 

6,501 

7,314 

8.8 

49 

14.5 

125 

46 

814.2 

1,628 

2,443 

3,257 

4,071 

4,886 

5,700 

6,514 

7,328 

8.9 

50 

14.6 

127 

47 

815.8 

1,  632. 

2,447 

3,263 

4,079 

4,895 

5,711 

6,  527 

7,  342 

9.0 

51 

14.7 

129 

48 

817.4 

1,635 

2,452 

3,270 

4,087 

4,904 

5,722 

6,539 

7,357 

9.1 

52 

14.8 

130 

49 

819.0 

1,638 

2,457 

3,276 

4,095 

4,914 

5,733 

6,552 

7,371 

9.2 

53 

14.9 

132 

50 

820.5 

1,641 

2,462 

3,282 

4,103 

4,923 

5,744 

6,564 

7,385 

9.3 

54 

15.0 

134 

51 

822.1 

1,644 

2,466 

3,288 

4,111 

4,933 

5,755 

6,577 

7,399 

9.4 

55 

15.1 

135 

52 

823.7 

1,647 

2,471 

3,295 

4,118 

4,  942 

5,766 

6,590 

7,  413 

9.5 

56 

15.2 

137 

53 

825.3 

1,651 

2,  476 

3,301 

4,126 

4,952 

5,777 

6,602 

7,427 

9.6 

58 

15.3 

139 

54 

826.8 

1,654 

2,  481 

3,307 

4,134 

4,961 

5,788 

6,615 

7,442 

9.7 

59 

15.4 

141 

55 

828.4 

1,657 

2,485 

3,314 

4,142 

4,970 

5,799 

6,627 

7,456 

9.8 

60 

15.5 

142 

66 

830.0 

1,660 

2,490 

3,320 

4,150 

4,980 

5,  810 

6,640 

7,470 

9.9 

81 

15.6 

144 

57 

831.5 

1,663 

2,495 

3,326 

4,158 

4,989 

5,821 

6,652 

7,484 

10.0 

62 

15.7 

146 

58 

833.1 

1,666 

2,  499 

3,332 

4,166 

4,999 

5,832 

6,  665 

7,498 

10.1 

63 

15.8 

148 

59 

834.7 

1,669 

2,504 

3,339 

4,173 

5,008 

5,843 

6,678 

7,512 

15.9 

150 

16.0 

151 

60 

836.3 

1,673 

2,509 

3,345 

4,181 

6,018 

5,854 

6,690 

7,526 

«  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. ' 


284  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — 'For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

9° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections   for   curva- 
ture,  refraction,    and 
height  of  instruments 

, 

0 

836.3 

1,673 

2,509 

3,345 

4,181 

5,018 

5,854 

6,690 

7,526 

1 

837.8 

1,676 

2,514 

3,351 

4,189 

5,027 

5,  865 

6,703 

7,541 

Miles. 

Feet. 

Miles. 

Feet. 

2 

839.4 

1,679 

2,  518 

3,358 

4,197 

5,037 

5,876 

6,715 

7,555 

1.6 

6 

10.2 

64 

3 

841.0 

1,  682 

2,523 

3,364 

4,  205 

5,046 

5,887 

6,  728 

7,569 

2.1 

7 

10.3 

65 

4 

842.6 

1,685 

2,528 

3,370 

4,213 

5,055 

5,898 

6,741 

7,583 

2.5 

8 

10.4 

67 

5 

844.2 

1,688 

2,532 

3,377 

4.  221 

5,  065 

5,909 

6,753 

7,  597 

2.8 

9 

10.5 

68 

6 

845.7 

1,691 

2,537 

3,  383 

4,229 

5,074 

5,920 

6,766 

7,612 

3.1 

10 

10.6 

69 

7 

847.3 

1,695 

2,542 

3,389 

4,237 

5,084 

5,931 

6,778 

7,626 

3.4 

11 

10.7 

70 

8 

848.9 

1,698 

2,547 

3,396 

4,244 

5,093 

5,  942 

6,791 

7,640 

3.6 

12 

10.8 

71 

9 

850.5 

1,701 

2,551 

3,  402 

4,252 

5,103 

5,953 

6,804 

7,654 

3.8 

13 

10.9 

73 

10 

852.0 

1,704 

2,556 

3,408 

4,260 

5,112 

5,964 

6,816 

7,668 

4.1 

14 

11.0         74 

11 

853.6 

1,707 

2,561 

3,414 

4,268 

5,122 

5,975 

6,829 

7,683 

4.3 

15 

11.1 

75 

12 

855.2 

1,710 

2,566 

3,421 

4,276 

5.  131 

5,986 

6,842 

7,697 

4.5 

16 

11.2 

77 

x3 

856.8 

1,714 

2,570 

3,427 

4,284     5!  141 

5,997 

6,854 

7,711 

4.7 

17 

11.3 

78 

14 

858.3 

1.717 

2,575 

3,433     4,292  1  5,150 

6,008 

6,867 

7,725 

4.8 

18 

11.4 

79 

15 

859.9 

1,720 

2,580 

3,440     4.300  |  5,160 

6,  020 

6,879 

7,739 

5.0 

19 

11.5 

80 

16 

861.5 

1,  723 

2,585 

3,446 

4,308  j  5,169 

6,031 

6,892 

7,754 

5.2 

20 

11.6 

82 

17 

863.1 

1,726 

2,589 

3,452 

4,315  !  5,179 

6,042 

6,905 

7,768 

5.4 

21 

11.7 

83 

18 

864.7 

1,729 

2,594 

3,459     4,323     5.188 

6,053 

6,917 

7,782 

5.5 

22 

1J.8 

84 

19 

866.2 

1,732 

2,  599 

3,465j  4,331 

5,197 

6,064 

6,930 

7,796 

5.7 

23 

11.9 

86 

20 

867.8 

1,736 

2,603 

3,471  j  4,339 

5,  207 

6,075 

6,943 

7,810 

5.8 

24 

12.0 

87 

21 

869.4 

1,739 

2,  608 

3,478     4,347 

5,216 

6,086 

6,  955 

7,  825 

6.0 

25 

12.1 

89 

22 

871.0 

1,742 

2,613 

3,484 

4,355 

5,226 

6,097 

6,968 

7,839 

6.1 

26 

12.2 

90 

23 

872.5 

1,745 

2,618 

3,490 

4,363 

5,235 

6,108 

6,  980     7,  853 

6.3 

27 

12.3 

91 

24 

874.1 

1,748 

2,  622 

3,496 

4,371 

5,245 

6,119 

6,993 

7,867 

6.4 

28 

12.4 

93 

25 

875.7 

1,751 

2,  627 

3,503 

4,379 

5,254 

6,130 

7,006 

7,881 

6.5 

29 

12.5 

94 

26 

877.3 

1,755 

2,  632 

3,509 

4,386 

5,264 

6,141 

7,018 

7,896 

6.7 

30 

12.6 

96 

27 

878.8 

1,758 

2,  637 

3,515 

4,394 

5,273 

6,  152 

7,031 

7,910 

6.8 

31 

12.7 

97 

28 

880.4 

1,761 

2,641 

3,522 

4,402 

5,283 

6,163 

7,043 

7,924 

6.9 

32 

12.8 

99 

29 

882.0 

1,764 

2,646 

3,528 

4,410 

5,  292 

6,174 

7,056 

7,938 

7.0 

33 

12.9 

100 

30 

883.6 

1,767 

2,651 

"3,534 

4,418 

5,302 

6,185 

7,068 

7,  952 

7.2 

34 

13.0 

102 

31 

885.2 

1,770 

2,  656 

3,541 

4,426 

5,311 

6,196     7.081 

7,967 

7.3 

35 

13.1 

103 

32 

886.7 

1,774 

2,660 

3,547 

4,434 

5,320 

6,207 

7,094 

7,981 

7.4 

36 

13.2 

105 

33 

888.3 

1,777 

2,665 

3,553 

4,442 

5,330 

6,218 

7,107 

7,995 

7.5 

37 

13.3 

106 

34 

889.9 

1,780 

2,670 

3,560 

4,450 

5,339 

6,229 

7,119 

8,009 

7.6 

3S 

13.4 

108 

35 

891.5 

1,783 

2,674 

3,566 

4,457 

5,349 

6.240     7,132 

8,023 

7.8 

39 

13.5 

109 

36 

893.1 

1,786 

2,679 

3,572 

4,465 

5,  358     6,  252 

7,145 

8,038 

7.9 

40 

13.6 

111 

37 

894.6 

1,789 

2,684 

3,579 

4,473 

5,368 

6,263 

7,157 

8,052 

8.0 

41 

13.7 

112 

38 

896.2 

1,792 

2,689 

3,585 

4,481 

5,377 

6,  274 

7,170 

8,066 

8.1 

42 

13.8 

114 

39 

897.8 

1,796 

2,693 

3,591 

4,489 

5,387 

6,285 

7,183 

8,080 

8.2 

43 

13.9 

115 

40 

899.4 

1,799 

2,698 

3,598 

4,497 

5,396 

6,296 

7,195 

8,095 

8.3 

44 

14.0 

117 

41 

901.0 

1,802 

2,  703     3,  604 

4,505 

5,406 

6,307 

7,208 

8,109 

8.4 

45 

14.1 

119 

42 

902.5 

1,805 

2,  708 

3,610 

4,513 

5,415 

6,318 

7,220 

8,123 

8.5 

46 

14.2 

120 

43 

•   904.1 

1,808 

2,712 

3,617 

4,  521 

5,425 

6,  329 

7,233 

8,137 

8.6 

47 

14.3 

122 

44 

905.7 

1,811 

2,717 

3,623 

4,529 

5,434 

6,340 

7,  246 

8,151 

8.7 

48 

14.4 

124 

45 

907.3 

1,814 

2,  722 

3,629 

4,537 

5,444 

6,351 

7,258 

8,166 

8.8 

49 

14.5 

125 

46 

908.9 

1,818 

2,727 

3,636 

4,544 

5,453 

6,362 

7,271 

8,180 

8.9 

50 

14.6 

127 

47 

910.5 

1,821 

2,731 

3,  642 

4,552 

5,463 

6,373 

7,284 

8,  194 

9.0 

51 

14.7 

129 

48 

912.0 

1,824 

2,736 

3,648 

4,560 

5,472 

6,384 

7,296 

8,208 

9.1 

52 

14.8 

130 

49 

913.6 

1,827 

2,  741 

3,654 

4,568 

5,482 

6,395 

7,309 

8,223 

9.2 

53 

14.9 

132 

50 

915.2 

1,830 

2,746 

3,661 

4,576 

5,491 

6,406 

7,322 

8,237 

9.3 

54 

15.0 

134 

51 

916.8 

1,833 

2,750 

3,667 

4,584 

5,501 

6,417 

7,334 

8,251 

9.4 

55 

15.1 

135 

52 

918.4 

1,837 

2,755 

3,673 

4,  592 

5,  510 

6,429 

7,347 

8,265 

9.5 

56 

15.2 

137 

53 

919.9 

1,840 

2,  760 

3,680 

4,600 

5,520 

6,440 

7,360 

8,279 

9.6 

58 

15.3 

139 

54 

921.5 

1,843 

2,  765 

3,686 

4,608 

5,  529 

6,451 

7,  372 

8,294 

9.7 

59 

15  4 

141 

55 

923.1 

1,846 

2,769 

3,692 

4,616 

5,539 

6,  462 

7,385 

8,308 

9.8 

60 

15.5 

142 

56 

924.7 

1,849 

2,774 

3,699 

4,623 

5,548 

6,473 

7,397 

8,  322 

9.9 

61 

15.6 

144 

57 

926.3 

1,852 

2,779 

3,705 

4,631 

5,558 

6,484 

7,410 

8,336 

10.0 

62 

15.7 

146 

58 

927.8 

1,855 

2,784 

3,711 

4,639 

5,567 

6,495 

7,423 

8,351 

10.1 

63 

15.8 

148 

59 

929.4 

1,859 

2,788 

3,718 

4,647 

5,577 

6,506 

7,435 

8,365 

15.9 

150 

16.0 

151 

60 

931.0 

1,862 

2,  793 

3,  724 

4,655 

5,586 

6,517 

7,448 

8,379 

«For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  285 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

10° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections  for  curva- 
ture, refraction    and 
height  of  instruments 

0 

931.0 

,862 

2,793 

3,724 

4,655 

5,586 

6,517 

7,448 

8,379 

1 

932.6 

,865 

2,798 

3,730 

4,663 

5,596 

6,528 

7,461 

8,393 

Miles. 

Feet. 

Miles. 

Feet. 

2 

934.2 

,868 

2,803 

3,737 

4,671 

5,605 

6,539 

7,473 

8,408 

1.6 

6 

10.2 

64 

3 

935.8 

,872 

2,807 

3,743 

4,679 

5,615 

6,550 

7,486 

8,422 

2.1 

7 

10.3 

65 

4 

937.4 

,875 

2,812 

3,749 

4,687 

5,624 

6,561 

7,499 

8,436 

2.5 

8 

10.4 

67 

5 

938.9 

,878 

2,817 

3,756 

4,695 

5,634 

6,573 

7,512 

8,450 

2.8 

9 

10.5 

68 

6 

940.5 

,881 

2,822 

3,  762 

4,703 

5,643 

6,584 

7,  524 

8,465 

3.1 

10 

10.6 

69 

7 

942.1 

,884 

2,826 

3,768 

4,711 

5,653 

6,595 

7,537 

8,479 

3.4 

11 

10.7 

70 

8 

943.7 

,887 

2,831 

3,775 

4,718 

5,662 

6,606 

7,  550 

8,493 

3.6 

12 

10.8 

71 

g 

945.3 

,891 

2,836 

3,781 

4,726 

5,672 

6,617 

7,562 

8,508 

3.8 

13 

10.9 

73 

10 

946.9 

,894 

2,841 

3,787 

4,734 

5,681 

6,628 

7,  575 

8,522 

4.1 

14 

11.0 

74 

11 

948.5 

,897 

2,845 

3,794 

4,742 

5,691 

6,639 

7,588 

8,536 

4.3 

15 

11.1 

75 

12 

950.0 

,900 

2,850 

3,800 

4,750 

5,700 

6,650 

7,600 

8,550 

4.5 

16 

11.2 

77 

13 

951.6 

,903 

2,855 

3,807 

4,758 

5,710 

6,661 

7,613 

8,565 

4.7 

17 

11.3 

78 

14 

953.2 

,906 

2,860 

3,813 

4,766 

5,719 

6,672 

7,626 

8,579 

4.8 

18 

11.4 

79 

15 

954.8 

,910 

2,864 

3,819 

4,774 

5,729 

6,684 

7,638 

8,593 

5.0 

19 

11.5 

80 

16 

956.4 

,913 

2,869 

3.  826 

4,782 

5,738 

6,695 

7,651 

8,607 

5.2 

20 

11.6 

82 

17 

958.0 

,916 

2,874     3;  832 

4,790 

5,748 

6,706 

7,664 

8,622 

5.4 

21 

11.7 

83 

IN 

959.6 

,919 

2,879     3,838 

4,798 

5,757 

6,217 

7,676 

8,636 

5.5 

22 

11.8 

84 

I'.i 

961.1 

,922 

2,  883     3,  845 

4,806 

5,767 

6,728 

7,689 

8,650 

6.7 

23 

11.9 

86 

20 

962.7 

.926 

2,888  '  3,851 

4,814 

5,776 

6,739 

7,702 

8,665 

5.8 

24 

12.0 

87 

21 

964.3  1     ^929 

2,893 

3,857 

4,  822 

5,786 

6,750 

7,715 

8,679 

6.0 

25 

12.1 

89 

22 

965.9 

,932 

2,898 

3,864 

4,830 

5,795 

6,751 

7,727 

8,693 

6.1 

26 

12.2 

90 

23 

967.5 

,935 

2,902 

3,870 

4,837 

5,805 

6,772 

7,740 

8,707 

6.3 

27 

12.3 

91 

24 

969.1 

,938 

2,907 

3,876 

4,845 

5,814 

6,784 

7,753 

8,722 

6.4 

28 

12.4 

93 

25 

970.7 

,941 

2,912 

3,883 

4,853 

5,824 

6,795 

7,765 

8,736 

6.5 

29 

12.5 

94 

26 

972.2 

,944 

2,917 

3,889 

4,861 

5,833 

6,806 

7,778 

8,750 

6.7 

30 

12.6 

96 

27 

'.'7:;.  s 

,948 

2,921 

3,895 

4,869 

5,843 

6,817 

7,791 

8,764 

6.8 

31 

12.7 

97 

2* 

975.4 

,951 

2,926 

3,902 

4  877 

5,853 

6,828 

7,803 

8,779 

6.9 

32 

12.8 

99 

29 

977.0 

,954 

2,931 

3,908 

4,885 

5,862 

6,839 

7,816 

8,793 

7.0 

33 

12.9 

100 

30 

978.6 

,957 

2,936 

3,914 

4,893 

5,872 

6,850 

7,829 

8,807 

7.2 

34 

13.0 

102 

31 

980.2 

,960 

2,941 

3,921 

4,901 

5,881 

6,861 

7,841 

8,822 

7.3 

35 

13.1 

103 

32 

981.8 

,964 

2,945 

3,927 

4,909 

5,891 

6,872 

7,854 

8,836 

7.4 

36 

13.2 

105 

33 

983.4 

,967 

2.950 

3,933 

4,917 

5,900 

6,884 

7,867 

8,850 

7.5 

37 

13.3 

106 

34         985.0 

,  970     2,  955 

3,940 

4,925 

5,910 

6,895 

7,880 

8,865 

7.6 

38 

13.4 

108 

35 

986.5 

,973 

2,960 

3,946 

4,933 

5,919 

6,906 

7,892 

8,879 

7.8 

39 

13.5 

109 

M 

988.1 

,976 

2,964 

3,953 

4,941 

5,929 

6,917 

7,905 

8,893 

7.9 

40 

13.6 

111 

37 

989.7 

,980 

2,969 

3,959 

4,949 

5,938 

6,928 

7,918 

8,908 

8.0 

41 

13.7 

112 

38 

991.3 

,983 

2,974 

3,965 

4,957 

5,948 

6,939 

7,931 

8,922 

8.1 

42 

13.8 

114 

39 

992.9 

,986 

2,979 

3,972 

4,965 

5,957 

6,950 

7,943 

8,936 

8.2 

43 

13.9 

115 

40 

994.5 

,989 

2,984 

3,978 

4,973 

5,967 

6,962 

7,956 

8,951 

8.3 

44 

14.0 

117 

41 

996.1 

,992 

2,988 

3,984 

4,980 

5,977 

6,973 

7,969 

8,965 

8.4 

45 

14.1 

119 

42 

997.7 

1,995 

2,993 

3,991 

4,988 

5,986 

6,984 

7,981 

8,979 

8.5 

46 

14.2 

120 

43 

999.3 

1,999 

2,998 

3,997 

4,996 

5,996 

6,995 

7,994 

8,993 

8.6 

47 

14.4 

122 

44 

1,000.9 

2,002 

3,003 

4,003 

5,004 

6,005 

7,006 

8,007 

9,008 

8.7 

48 

14.3 

124 

45 

1,002.5 

2,  005 

3,007 

4,010 

5,012 

6,  015 

7,  017     8,  020 

9,022 

8.8 

49 

14.5 

125 

46 

1,004.0 

2,008 

3,012 

4,016 

5,  020 

6,021 

7,028 

8,032 

9,036 

8.9 

50 

14.6 

127 

47 

1,005.6 

2,011 

3,017 

4,023 

5,028 

6,034 

7,039 

8,045 

9,051 

9.0 

51 

14.7 

129 

48 

1,007.2 

2,014 

3,022 

4,029 

5,036 

6,043 

7,051 

8,058 

9,065 

9.1 

52 

14.8 

130 

49 

1,008.8 

2,018 

3,026 

4,035 

5,044 

6,053 

7,062 

8,071 

9,079 

9.2 

53 

14.9 

132 

50 

1,010.4     2,021 

3,031 

4,042 

5,052 

6,062 

7,073     8,083 

9,094 

9.3 

54 

15.0 

134 

51 

1,012.0     2,024 

3,036 

4,048 

5,060 

6,072 

7,084     8,096 

9,108 

9.4 

55 

15.1 

135 

52 

1,013.6     2,027     3,041 

4,054 

5,068 

6,082 

7,095  1  8,109 

9,122 

9.5 

56 

15.2 

137 

58 

1,015.2 

2,030     3,046 

4,061 

5,076 

6,091 

7,106  |  8,121 

9,137 

9.6 

58 

16.3 

139 

54 

1,016.8 

2,  034     3,  050 

4,067     5.084 

6,101 

7,117     8,134 

9,151 

9.7 

59 

15.4 

141 

55 

1,018.4 

2,037     3,055 

4,073 

5,092 

6,110 

7,  129     8,  147 

9,165 

9.8 

60 

15.5 

142 

61 

1,020.0 

2,040  j  3,060 

4,080 

5,100 

6,120 

7,140 

8,160 

9,180 

9.9 

61 

15.6 

144 

57 

1,  021.  5 

2,043  !  3,065 

4,086 

5,108 

6,129 

7,151 

8,172 

9,194 

10.0 

62 

15.7 

146 

58 

1,023.1 

2,  046     3,  069 

4,093 

5,116 

6,139 

7,162 

8,185 

9,208 

10.1 

63 

15.8 

148 

59 

1,024.7 

2,049 

3,074 

4,099 

5,124 

6,148 

7,173 

8,198 

9,223 

15.9 

150 

16.0 

151 

60 

1,026.3 

2,053 

3,079 

4,105 

5,132 

6,158 

7,184 

8,211 

9,237 

1 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


286  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

11° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections  for  curva- 
ture, refraction,   and 
height  of  instrument,  a 

0 

1,  026.  3 

2,053 

3,079 

4,105 

5,132 

6,158 

7,184 

8,211 

9,237 

1 

1,027.9 

2,056 

3,084 

4,112 

5,140 

6,168 

7,195 

8,223 

9,251 

Miles. 

Feet. 

Miles. 

Feet. 

2 

1,029.5!  2,059 

3,089 

4,118 

5,148 

6,177 

7,207 

8,236 

9,266 

1.6 

6 

10.2 

64 

3 

1,031.1|  2,062 

3,093 

4,124 

5,156 

6,187 

7,218 

8,249 

9,280 

2.1 

7 

10.3 

65 

4 

1,  032.  7 

2,065 

3,098 

4,131 

5,164 

6,196 

7,229 

8,262 

9,294 

2.5 

8 

10.4 

67 

5 

1,  034.  3 

2,069 

3,103 

4,137 

5,172 

6,206 

7,240 

8,  275 

9,309 

2.8 

9 

10.5 

68 

6 

1,036 

2,072 

3,108 

4,144 

5,180 

6,215 

7,251 

8,287 

9,323 

3.1 

10 

10.6 

69 

7 

1,038 

2,075 

3,113 

4,150 

5,188 

6,225 

7,263 

8,300 

9,338 

3.4 

11 

10.7 

70. 

8 

1,039 

2,078 

3,117 

4,156 

5,196 

6,235 

7,274 

8,313 

9,352 

3.6 

12 

10.8 

71 

9 

1,041 

2,081 

3,122 

4,163 

5,204 

6,244 

7,285 

8,326 

9,366' 

3.8 

13 

10.9 

73 

10 

1,042 

2,085 

3,127 

4,169 

5,212 

6,254 

7,296 

8,338 

9,381 

4.1 

14 

11.0 

74 

11 

1,044 

2,088 

3,132 

4,176 

5,219 

6,263 

7,307 

8,351 

9,395 

4.3 

15 

11.1 

75 

12 

1,045 

2,091 

3,136 

4,182 

5,  227 

6,273 

7,318 

8,364 

9,409 

4.5 

16 

11.2 

77 

13 

1,047 

2,094 

3,141 

4,188 

5,235 

6,283 

7;  330 

8,377 

9,424 

4.7 

17 

11.3 

78 

14 

1,049 

2,  097 

3,146 

4,195 

5,243 

6,292 

7,341 

8,390 

9,438 

4.8 

18 

11.4 

79 

15 

1,050 

2,101 

3,151 

4,201 

5,251 

6,302 

7,352 

8,402 

9,453 

5.0 

19 

11.5 

80 

16 

1,052 

2,104 

3,156 

4,208 

5,259 

6,311 

7,363 

8,415 

9,467 

5.2 

20 

11.6 

82 

17 

1,053 

2,107 

3,160 

4,214 

5,  267 

6,321 

7,374 

8,428 

8,481 

5.4 

21 

11.7 

83 

18 

1,055 

2,110 

3,165 

4,220 

5,275 

6,330 

7,386 

8,441 

9,  496       5.  5 

22 

11.8 

84 

19 

1,057 

2,113 

3,170 

4,227 

5,283 

6,340 

7,397 

8,453 

9,510  i     5.7 

23 

11.9 

86 

20 

1,058 

2,117 

3,176 

,233 

5,291 

6,350 

7,408 

8,466 

9,524 

5.8 

24 

12.0 

87 

21 

1,060 

2,120 

3,180 

,239 

5,299 

6,359 

7,419 

8,479 

9,539 

6.0 

25 

12.1 

89 

22 

1,061 

2,123 

3,184 

4,246 

5,307 

6,369 

7,430 

8,492 

9,553 

6.1 

26 

12.2 

90 

23 

1,063 

2,126 

3,189 

,252 

5,315 

6,378 

7,441 

8,504 

9,568 

6.3 

27 

12.3 

91 

24 

1,065 

2,129 

3,194 

,259 

5,323 

6,388 

7,453 

8,517 

9,582 

6.4 

28 

12.4 

93 

25 

1,066 

2,133 

3,199 

4,265 

5,331 

6,398 

7,464 

8,530 

9,596 

6.5 

29 

12.5 

94 

26 

1,068 

2,136 

3,204 

4,271 

5,339 

6,407 

7,475 

8,543 

9,611 

6.7 

30 

12.6 

96 

27 

1,069 

2,139 

3,208 

4,278 

5,347 

6,417 

7,486 

8,556 

9,  625 

6.8 

31 

12.7 

97 

28 

1,071 

2,142 

3,213 

5,  355 

6,426 

7,497 

8,568 

9,639 

6.9 

32 

12.8 

99 

29 

1,073 

2,145 

3,218 

4^291 

5,363 

6,436 

7,509 

8,581 

9,654 

7.0 

33 

12.9 

100 

30 

1,074 

2,148 

3,223 

4,297 

5,371 

6,445 

7,520 

8,594 

9,668 

7.2 

34 

13.0 

102 

31 

1,076 

2,152 

3,227 

4,303 

5,379 

6,455 

7,531 

8,607 

9,682 

7.3 

35 

13.1 

103 

32 

1,077 

2,156 

3,232 

4,310 

5,387 

6,465 

7,542 

8,619 

9,697 

7.4 

36 

13.2 

105 

33 

1,079 

2,158 

3,237 

4,316 

5,395 

6,474 

7,553 

8,632 

9,711 

7.5 

37 

13.3 

106 

34 

1,081 

2,161 

3,  242 

4,323 

5,  403 

6,484 

7,564 

8,645 

9,726 

7.6 

38 

13.4 

108 

35 

1,082 

2,164 

3,247 

4,329 

5,411 

6,493 

7,576 

8,658 

9,740 

7.8 

39 

13.5 

109 

36 

1,084 

2,168 

3,252 

4,335 

5,419 

6,503 

7.587 

8,671 

9,755 

7.9 

40 

13.6 

111 

37 

1,085 

2,171 

3,256 

4,342 

5,427 

6,513 

7,598 

8,683 

9,769 

8.0 

41 

13.7 

112 

38 

1,087 

2,174 

3,261 

4,348 

5,435 

6,522 

7,609 

8,696 

9,783 

8.1 

42 

13.8 

114 

39 

1,089 

2,177 

3,266 

4,355 

5,443 

6,532 

7,621 

8,709 

9,798 

8.2 

43 

13.9 

115 

40 

1,090 

2,181 

3,271 

4,361 

5,451 

6,542 

7,632 

8,722 

9,812 

8.3 

44 

14.0 

117 

41 

1,092 

2,184 

3,276 

4,367 

5,459 

6,551 

7,643 

8,  735 

9,827 

8.4 

45 

14.1 

119 

42 

1,093 

2,187 

3,280 

4,374 

5,467 

6,561 

7,654 

8,748 

9,841 

8.5 

46 

14.2 

120 

43 

1,095 

2,190 

3,285 

4,380 

5,475 

6,570 

7,665 

8,760 

9,856 

8.6 

47 

14.3 

122 

44 

1,097 

2,193 

3,290 

4,387 

5,483 

6,580 

7,677 

8,773 

9,870 

8.7 

48 

14.4 

124 

45 

1,098 

2,197 

3,295 

4,393 

5,491 

6,590 

7,688 

8,786 

9,884 

8.8 

49 

14.5 

125 

46 

1,100 

2,200 

3,300 

4,399 

5,499 

6,599 

7,699 

8,799 

9,899 

8.9 

50 

14.6 

127 

47 

1,101 

2,203 

3,304 

4,406 

5,507 

6,609 

7,710 

8,812 

9,913 

9.0 

51 

14.7 

129 

48 

1,103 

2,206 

3,309 

4,412 

5,515 

6,618 

7,721 

8,825 

9,928 

9.1 

52 

14.8 

130 

49 

1,  105 

2,209 

3,314 

4,419 

5,  523 

6,628 

7,733 

8,837 

9,942 

9.2 

53 

14.9 

132 

50 

1,106 

2,213 

3,319 

4,425 

5,531 

6,638 

7,744 

8,850 

9,956 

9.3 

54 

15.0 

134 

51 

1,108 

2,216 

3,324 

4,431 

5,539 

6,647 

7,755 

8,863 

9,971 

9.4 

55 

15.1 

135 

52 

1,109 

2,219 

3,328 

4,438 

5,547 

6,  657 

7,766 

8,876 

9,985 

9.5 

56 

15.2 

137 

53 

1,111 

2,222 

3,333 

4,444 

5,555 

6,666 

7,778 

8,889 

10,  000 

9.6 

58 

15.3 

139 

54 

1,113 

2,225 

3,338 

4,451 

5,563 

6,676 

7,789 

8,901 

10,  014 

9.7 

59 

15.4 

141 

55 

1,114 

2,229 

3,343 

4,457 

5,571 

6,686 

7,800 

8,914 

10,  029 

9.8 

60 

15.5 

142 

56 

1,116 

2,232 

3,348 

4,464 

5,579 

6,695 

7,811 

8,927 

10,  043 

9.9 

61 

15.6 

144 

57 

1,117 

2,235 

3,352 

4,470 

5,587 

6,705 

7,  822 

8,940 

10,  057 

10.0 

62 

15.7 

146 

58 

1,119 

2,238 

3,357 

4,476 

5,595 

•6,  715 

7,834 

8,953 

10,  072 

10.1 

63 

15.8 

148 

59 

1,  121 

2,241 

3,362 

4,483 

5,603 

6,724 

7,845 

8,966 

10,  086 

15.9 
16.0 

150 
151 

60 

1,122 

2,245 

3,367 

4,489 

5,611 

6,734 

7,856 

8,978 

10,101 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  287 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc.  —Continued. 

12° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections   for  curva- 
ture,  refraction,  and 
height  of  instruments 

0 

1,122 

2,245 

3,367 

4,489 

5,612 

6,734 

7,856 

8,978 

10,  101 

1 

1,124 

2,248 

3,372 

4,496 

5,620 

6,743 

7,867 

8,991 

10,115 

Miles. 

Feet. 

Miles. 

Feet. 

2 

1,126 

2,251 

3,377 

4,502 

5,  628 

6,753 

7,879 

9,004 

10,  130 

1.6 

6 

10.2 

64 

3 

1,127 

2,254 

3,381 

4,508 

5,636 

6,763 

7,890 

9,017 

10,  144 

2.1 

7 

10.3 

65 

4 

1,129 

2,257 

3,386 

4,515 

5,644 

6,772 

7,901 

9.030 

10,  159 

2.5 

8 

10.4 

67 

5 

1,130 

2,261 

3,391 

4,521 

5,652 

6,782 

7,912 

9,043 

10,  173 

2.8 

9 

10.5 

68 

6     1J132 

2,264 

3,396 

4,528 

5,660 

6,  792 

7,924 

9,056 

10,188 

.3.1 

10 

10.6 

69 

7 

1,134 

2,  267 

3,401 

4,534 

5,668 

6,801 

7,935 

9,068 

10,  202 

3.4 

11 

10.7 

70 

8 

1,135 

2,270 

3,405 

4,541 

5,676 

6,811 

7,946 

9,081 

10,  216 

3.6 

12 

10.8 

71 

9 

1,137 

2,274 

3,410 

4,547 

5,684 

6,821 

7,957 

9,094 

10,  231 

3.8 

13 

10.9 

73 

10 

1,138 

2,277 

3,415 

4,554 

5,692 

6,830 

7,969 

9,107 

10,  245 

4.1 

14 

11.0 

74 

11 

1,140 

2,280 

3,420 

4,560 

5,700 

6,840 

7,980 

9,  120 

10,  260 

4.3 

15 

11.1 

75 

12     1,  142 

2,283 

3,425 

4,566 

5,708 

6,850 

7,991 

9,133 

10,  274 

4.5 

16 

11.2 

77 

13     1,143 

2,286 

3,430 

4,573 

5,716 

6,859 

8,002 

9,146 

10,  289 

4.7 

17 

11.3 

78 

14     1,  145 

2,290 

3,434 

4,579 

5,  724 

6,869 

8,014 

9,158 

10,303 

4.8 

18 

11.4 

79 

15     1,146 

2,293 

3,439 

4,586 

5,732 

6,879 

8,025 

9,171 

10,318 

•5.0 

19 

11.5 

80 

16 

1,148 

2,296 

3,444 

4,592 

5,740 

(i,  NSS 

8,036 

9,184 

10,  332 

5.2 

20 

11.6 

U2 

17 

1,150 

2,299 

3,449     4;599 

5,  748     6.  898 

8,047     9,197 

10,  347 

5.4 

21 

11.7 

83 

18 

1,151 

2,302 

3,  4-54 

4,605 

5,756 

6,907 

8,059 

9,210 

10,  361 

5.5 

22 

11.8 

84 

19 

1,153 

2,306 

3,459 

4,611 

5,764 

6,917 

8,070 

9,223 

10,  376 

5.7 

23 

11.9 

86 

20 

1,154 

2,309 

3,463     4,618 

5,772 

6,927 

8,081 

9,236 

10,390 

5.8 

24 

12.0 

.  87 

21 

1,156 

2,312 

3,468 

4,624 

5,780 

6,936 

8,092 

9,249 

10,405 

6.0 

25 

12.1 

89 

22 

1,158 

2,315 

3,473 

4,631 

5,788 

6,946 

8,104 

9,261 

10,419 

6.1 

26 

12.2 

90 

23 

1,159 

2,319 

3,478 

4,637 

5,796 

6,956 

8,115 

9,274 

10,  434 

6.3 

27 

12.3 

91 

24 

1,161 

2,  322 

3,483     4,644 

5,804 

6,  965 

8,126 

9,287 

10,448 

6.4 

28 

12.4 

93 

25 

1,163 

2,  325 

3,487     4,650 

5,812 

6,975 

8,138 

9,300 

10,  463 

6.5 

29 

12.5 

94 

26 

1,164 

2,328 

3,492 

4,656     5,821 

6,985 

8,149 

9,  313     10,  477 

6.7 

30 

12.6 

96 

27 

1,166 

2,331 

3,497 

4,663     5,829 

6,994 

8,160 

9,326 

10,  491 

6.8 

31 

12.7 

97 

28 

1,167 

2,335 

3,502 

4,669     5,837 

7,004 

8,171 

9,339 

10,  506 

6.9 

32 

12.8 

99 

29 

1,169 

2,338 

3,507 

4,676     5,845 

7,014 

8,183 

9,351 

10,  520 

7.0 

33 

12.9 

100 

30 

1,171 

2,341 

3,512 

4,  682     5,  853 

7,023 

8,194 

9,364 

10,535 

7.2 

34 

13.0 

102 

31 

1,172 

2,344 

3,516 

4,  689     5,  861 

7,033 

8,205 

9,377 

10,549 

7.3 

35 

13.1 

103 

32 

1,174 

2,348 

3,521 

4,  695     5,  869 

7,043 

8,216 

9,390 

10,564 

7.4 

36 

13.2 

105 

33 

1,175 

2,351 

3,526 

4,  702     5,  877 

7,052 

8,228 

9,403 

10,  579 

7.5 

37 

13.3 

106 

34 

1,177 

2,354 

3,531 

4,708  !  5,885 

7,062 

8,239 

9,416 

10,  593 

7.6 

38 

13.4 

108 

86 

1,179 

2,357 

3,536 

4,  714     5,  893 

7,072 

8,250 

9,429 

10,  608 

7.8 

39 

13.5 

109 

36 

1,180 

2,360 

3,541 

4,  721     5,  901 

7,081 

8,262 

9,442 

10,  622 

7.9 

40 

13.6 

111 

37 

1,182 

2,364 

3,546 

4,727  |  5,909 

7,091 

8,273 

9,455 

10,  637 

8.0 

41 

13.7 

112 

38 

1,183 

2,367 

3,550 

4,734     5,917 

7,101 

8,284 

9,468 

10,  651 

8.1 

42 

13.8 

114 

39 

1,185 

2,370 

3,555 

4,740 

5,925 

7,110 

8,296 

9,481 

10,  666 

8.2 

43 

13.9 

115 

40 

1,187 

2,373 

3,560 

4,747 

5,933 

7,120 

8,307 

9,494 

10,680 

8.3 

44 

14.0 

117 

41 

1,188 

2,377 

3,565 

4,753 

5,  942 

7,130 

8,318 

9,506 

10,  695 

8.4 

45 

14.1 

119 

42 

1,190 

2,380 

3,  570 

4,760 

5,950 

7,140 

8,329 

9,519 

10,709 

8.5 

46 

14.2 

120 

48 

1,192 

2,383 

3,  575 

4,766 

5,  958 

7,149 

8,341 

9,  532 

10,  724 

8.6 

47 

14.3 

122 

1    44 

1,193 

2,386 

3,579 

4,773 

5,966 

7,159 

8,352 

9,545 

10,  738 

8.7 

48 

14.4 

124 

45 

1,196 

2,390 

3,584 

4,779 

5,974 

7,169 

8,363 

9,558 

10,  753 

8.8 

49 

14.5 

125 

H 

1,196 

2,393 

3,589 

4,  785 

ft,  982 

7,178 

8,375 

9,  571 

10,  767 

8.9 

50 

14.6 

127 

47 

1,198 

2,3% 

3,  594 

4,792 

5,  990 

7,188 

8,386 

9,584 

10,  782 

9.0 

51 

14.7 

129 

48 

1,200 

2,399 

3,599 

4,798 

5,998 

7,198 

8,397 

9,597 

10,  796 

9.1 

52 

14.8 

130 

49 

1,201 

2,402 

3,604 

4,805 

6,006 

7,207 

8,409 

9,610 

10,  811 

9.2 

53 

14.9 

132 

50 

1,203 

2,406 

3,608 

4,811 

6,014 

7,217 

8,420 

9,623 

10,  825 

9.3 

54 

15.0 

134 

51     1,  204 

2,409 

3,613 

4,818 

6,022 

7,227 

8,431 

9,636 

10,  840 

9.4 

55 

15.1 

135 

52 

1,206 

2,412 

3,618 

4,824 

6,030 

7,236 

8,442 

9,648 

10,  855 

9.5 

56 

15.2 

137 

53 

1,208 

2,415 

3,623 

4,831 

6,038 

7,246 

8,454 

9,661 

10,  869 

9.6 

58 

15.3 

139 

54 

1,209 

2,419 

3,628 

4,837 

6,046 

7,256 

8,465 

9,674 

10,884 

9.7 

59 

15.4 

141 

55 

1,211 

2,422 

3,633 

4,844 

6,055 

7,265 

8,476 

9,687 

10,  898 

9.8 

60 

15.5 

142 

56 

1,213 

2,425 

3,638 

4,8.50 

6,063 

7,275 

8,488 

9,700 

10,  913 

9.9 

61 

15.6 

144 

57 

1,214 

2,428 

3,642 

4,857 

6,071 

7,285 

8,499 

9,713 

10,  927 

10.0 

62 

15.7 

146 

58 

1,216 

2,431 

3,647 

4,863 

6,079 

7,294 

8,510 

9,726 

10,  942 

10.1 

63 

15.8 

148 

59 

1,217 

2,435 

3,652 

4,869 

6,087 

7,304 

8,521 

9,739 

10,  956 

15.9 

150 

16.0 

151 

60 

1,219 

2,438 

3,657 

4,876 

6,095 

7,314 

8,533 

9,752 

10,  971 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  6  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


288  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

13° 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Corrections  for  curva- 
ture, refraction,  and 
height  of  instruments 

0 

1,219 

2,438 

3,657 

4,876 

6,095 

7,314 

8,533 

9,752 

10,  971 

1 

1,221 

2,  441 

3,662 

4,882 

6,103 

7,324 

8,544 

9,765 

10,  985 

Miles. 

Feet. 

Miles. 

Feet. 

2 

1,222 

2,444 

3,667 

4,889 

6,111 

7,333 

8,  556 

9,778 

11,000 

1.6 

6 

10.2 

64 

3 

1,224 

2,448 

3,672 

4,895 

6,119 

7,343 

8,567 

9,791 

11,015 

2.1 

7 

10.3 

65 

4 

1,225 

2,451 

3,676 

4,902 

6,  127 

7,353 

8,578 

9,804 

11,029 

2.5 

8 

10.4 

67 

5 

1,227 

2,454 

3,681 

4,908 

6,135 

7,362 

8,590 

9,817 

11,044 

2.8 

9 

10.5 

68 

6 

1,229 

2,457 

3,686 

4,  915 

6,143 

7,372 

8,601 

9,830 

11,058 

3.1 

10 

10.6 

69 

7 

1,230 

2,461 

3,691 

4,921 

6,152 

7,382 

8,612 

9,843 

11,073 

3.4 

11 

10.7 

70 

8 

1,232 

2,464 

3,696 

4,928 

6,160 

7,392 

8,624 

9,855 

11,  087 

3.6 

12 

10.8 

71 

9 

1,234 

2,467 

3,701 

4,934 

6,168 

7,401 

8,635 

9,868 

11,  102 

3.8 

13 

10.9 

73 

10 

1,235 

2,470 

3,706 

4,941 

6,176 

7,411 

8,646 

9,881 

11,117 

4.1 

14 

11.0 

74 

11 

1,237 

2,474 

-3,710 

4,947 

6,184 

7,421 

8,658 

9,894 

11,  131 

4.3 

15 

11.1 

75 

12 

1,238 

2,477 

3,  715 

,954 

6,192 

7,430 

8,669 

9,907 

11,146 

4.5 

16 

11.2 

77 

13 

1,240 

2,480 

3,720 

,960 

6,200 

7,440 

8,680 

9,920 

11,  160 

4.7 

17 

11.3 

78 

14 

1,243 

2,483 

3,725 

,967 

6,  208 

7,450 

8,692 

9,933 

11,175 

4.8 

18 

11.4 

79 

15 

1,243 

2,487 

3,730 

,973 

6,216 

7,460 

8,703 

9,946 

11,190 

5.0 

19 

11.5 

80 

16 

1,245 

2,490 

3,735 

,980 

6,224 

7,469 

8,714 

9,959 

11,204 

5.2 

20 

11.6 

82 

17 

1,247 

2,493 

3,740 

,986 

6,233 

7,479 

8,726 

9,972 

11,219 

5.4 

21 

11.7 

83 

18 

1,248 

2,496 

3,744 

4,993 

6,  241 

7,489 

8,737 

9,985 

11,233 

5.5 

22 

11.8 

84 

19 

1,250 

2,500 

3,749 

4,999 

6,249 

7,499 

8,748 

9,998 

11,248 

5.7 

23 

11.9 

86 

20 

1,251 

2,503 

3,754 

5,006 

6,257 

7,508 

8,760 

10,011 

11,262 

5.8 

24 

12.0 

87 

21 

1,253 

2,506 

3,759 

5,012 

6,265 

7,518 

8,  771  10;  024 

11,277 

6.0 

25 

12.1 

89 

22 

1,255 

2,509 

3,764 

5,019 

6,273 

7,528 

8,782 

10,  037 

11,  292 

6.1 

26 

12.2 

90 

23 

1,256 

2,513 

3,769 

5,025 

6,281 

7,537 

8,794 

10,050 

11,306 

6.3 

27 

12.3 

91 

24 

1,258 

2,516 

3,774 

5,032 

6,  289 

7,547 

8,  805 

10,063 

11,  321 

6.4 

28 

12.4 

93 

25 

1,260 

2,519 

3,779 

5,038 

6;  297 

7,  557 

8,816 

10,  076 

11,336 

6.5 

29 

12.5 

94 

20 

1,261 

2,522 

3,783 

5,044 

6,306 

7,567 

8,828 

10,  089 

11,350 

6.7 

30 

12.6 

96 

27 

1,263 

2,  525 

3,788 

5,051 

6,314 

7,576 

8,839 

10,  102 

11,365 

6.8 

31 

12.7 

97 

28 

1,264 

2,529 

3,793 

5,057 

6,322 

7,586 

8,851 

10,115 

11,379 

6.9 

32 

12.8 

99 

29 

1,266 

2,532 

3,798 

5,064 

6,330 

7,596 

8,862 

10,  128 

11,394 

7.0 

33 

12.9 

100 

30 

1,268 

2,535 

3,803 

5,070 

6,338 

7,606 

8,873 

10,  141 

11,409 

7.2 

34 

13.0 

102 

31 

1,269 

2,538 

3,808 

5,077 

6,346 

7,615 

8,885 

10,154 

11,423 

7.3 

35 

13.1 

103 

32 

1,271 

2,642 

3,813 

5,083  1  6,354 

7,625 

8,896 

10,  167 

11,438 

7.4 

36 

13.2 

105 

33 

1,273 

2,545 

3,817 

5,090  6,362 

7,635 

8,907 

10,180 

11,  452 

7.5 

37 

13.3 

106 

34 

1,274 

2,548 

3,822 

5,  096  6,  371 

7,645 

8,919 

10,  193 

11,467 

7.6 

38 

13.4 

108 

35 

1,276 

2,551 

3,827 

5,103 

6,379 

7,  654  8,  930 

10,206 

11,482 

7.8 

39 

13.5 

109 

36 

1,277 

2,555 

3,832 

5,109 

6,387 

7,664  8,942 

10,  219 

11,  496 

7.9 

40 

13.6 

111 

37 

1,279 

2,558 

3,837 

5,116 

6,395 

7,674  I  8,953 

10,  232 

11,  511 

8.0 

41 

13.7 

112 

38 

1,281 

2,561 

3,842 

5,122 

6,403 

7,  684  8,  964 

10,  245 

11,526 

8.1 

42 

13.8 

114 

39 

1,282 

2,565 

3,847 

5,129 

6,411 

7,693 

8,976 

10,258 

11,540 

8.2 

43 

13.9 

115 

40 

1,284 

2,568 

3,852 

5,135 

6,419 

7,703 

8,987 

10,  271 

11,555 

•8.3 

44 

14.0 

117 

41 

1,286 

2,571 

3.857 

5,142 

6,427 

7,713 

8,999 

10,  284 

11,  569 

8.4 

45 

14.1 

119 

42 

1,287 

2,  574 

3,861 

5,149 

6,436 

7,723 

9,010 

10,  297 

11,584 

8.5 

46 

14.2 

120 

43 

1,289 

2,578 

3,866 

5,155 

6,444 

7,732 

9,021 

10,  310 

11,599 

8.6 

47 

14.3 

122 

44 

1,290 

2,581 

3,871 

5,162 

6,452 

7,742 

9,033 

10,323 

11,613 

8.7 

48 

14.4 

124 

45 

1,292 

2,584 

3,876 

5,168 

6,460 

7,752 

9,044 

10,  336 

11,628 

8.8 

49 

14.5 

125 

46 

1,294 

2,587 

3,881 

5,  175 

6,468 

7,762 

9,055 

10,349 

11,  643 

8.9 

50 

14.6 

127 

47 

1,  295 

2,591 

3,886 

5,  181 

6,476 

7,771 

9,067 

10,362 

11,  657 

9.0 

51 

14.7 

120 

48 

1,297 

2,594 

3,891 

5,188 

6,484 

7,781 

9,078 

10,  375 

11,672 

9.1 

52 

14.8 

130 

49 

1,299 

2,597 

3,896 

5,194 

6,4^3 

7,791 

9,090 

10,388 

11,687 

9.2 

53 

14.9 

132 

50 

1,300 

2,600 

3.900 

5,201 

6,501 

7,801 

9,101 

10",  401 

11,701 

9.3 

54 

15.0 

134 

51 

1,302 

2,604 

3,905 

5,207 

6,509 

7,811 

9,112 

10,  414 

11,716 

9.4 

55 

15.1 

135 

52 

1,303 

2,607 

3,910 

5,  214 

6,517 

7,820 

9,124 

10,427 

11,  731 

9.5 

56 

15.2 

137 

5a 

1,305 

2,610 

3,915 

5,220 

6,  525 

7,830 

9,135 

10,  440 

11,  745 

9.6 

58 

15.3- 

139 

54 

1,307 

2,613 

3,920 

5,227 

6,533 

7,840 

9,147 

10,453 

11,760 

9.7 

59 

15.4 

141 

65 

1,308 

2,617 

3,925 

5,233 

6,541 

7,850 

9,158 

10,  466 

11,775 

9.8 

60 

15.5 

142 

56 

1,310 

2,620 

3,930 

5,240 

6,550 

7,859 

9,170 

10,479 

11,789   9.9 

61 

15.6 

144 

67 

1,312 

2,623 

3,935 

5,246 

6,558 

7,869 

9,181 

10,492 

11,804  '  10.0 

62 

15.7 

146 

58 

1,313 

2,626 

3,940 

5,253 

6,566 

7,879 

9,192 

10,506 

11,819 

10.1 

63 

15.8 

148 

59 

1,315 

2,630 

3,944 

5,259 

6,574 

7,889 

9,204 

10,  519 

11,  833 

15.9 

150 

16.0  |  151 

60 

1,316 

2,633 

3,949 

5,266 

6,582 

7,899 

9,215 

10,532 

11,848 

| 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


GEOGRAPHIC    TABLES    AND    FORMULAS.  289 

TABLE  27. — For  obtaining  differences  of  altitude  for  any  minute,  etc. — Continued. 

14° 


1 

'-> 

8 

9 

Corrections   for   curva- 
ture, refraction,  and 
height  of  iiistrument.a 

0 

1,316 

2,633 

3,949 

5,266 

6,582 

7,899 

9,215 

10,632 

11,848 

1 

1,318 

2,636 

3,954 

5,272 

6,590 

7,909 

9,227 

10,545 

11,863 

Miles. 

feet. 

Miles. 

Feet. 

2 

1,320 

2,639 

3,959 

5,279 

6,599 

7,918 

9,238 

10,558 

11,  877 

1.6 

6 

10.2 

64 

3 

1,321 

2,643 

3,964 

5,285 

6,607 

7,928 

9,249 

10,571 

11,892 

2.1 

7 

10.3 

65 

4 

1,323 

2,646 

3,969 

5,292 

6,615 

7,938 

9,261 

10,584 

11,  907 

2.5 

8 

10.4 

67 

5 

1,325 

2,649 

3,974 

5,298 

6.623 

7,948 

9,272 

10,  597 

11,923 

2.8 

9 

10.5 

68 

6 

1,326 

2,653 

3,979 

5,305 

6,631 

7,957 

9,284 

10,  610 

11,93(5 

3.1 

10 

10.6 

69 

7 

1,328 

2,656 

3,984 

•5,  312 

6,639 

7,967 

9,295 

10,  623 

11,  951 

3.4 

11 

10.7 

70 

8 

1,330 

2,659 

3,989 

5,318 

6,648 

7,977 

9,307 

10,636 

11,966 

3.6 

12 

10.8 

71 

9 

1,331 

2,662 

3,993 

5,325 

6,656 

7,987 

9,318 

10,649 

11,  980 

3.8 

13 

10.9 

73 

10 

1,333 

2,666 

3,998 

5,331 

6,664 

7,997 

9,329 

10,662 

11,995 

4.1 

14 

11.0 

74 

11 

1,334 

2,669 

4,003 

5,338 

6,  672 

8,006 

9,341 

10,  675 

12,  010 

4.3 

15 

11.1 

75 

12 

1,336 

2,672 

,008 

5,344 

6,680 

8,016 

9,  352 

10,688 

12,024 

4.5 

16 

11.2 

77 

13 

1,338 

2,675 

,013 

5,351 

6,688 

8,026 

9,364 

10,  701 

12,  039 

4.7 

17 

11.3 

78 

14 

1,339 

2,679 

,018 

5,357 

6,697 

8,036 

9,375 

10,  715 

12,054 

4.8 

18 

11.4 

79 

15 

1,341 

2,682 

,023 

5,364 

6,706 

8,046 

9,387 

10,  728 

12,069 

5.0 

19 

11.5 

80 

16 

1,343 

2,686 

,028 

5,370 

6,713 

8,056 

9,398 

10,741 

12,  083 

5.2 

20 

11.6 

82 

17 

1,344 

2,688 

,033 

5,377 

6,721 

8,065 

9,410 

10,  754 

12,  098 

5.4 

21 

11.7 

83 

18 

1,346 

2,692 

,038 

5,383 

6,729 

8,075 

9,421 

10,  767 

12,  113 

5.5 

22 

11.8 

84 

19 

1,348 

2,695 

,042 

5,390 

6,737 

8,085 

9,432 

10,780 

12,  127 

5.7 

23 

11.9 

86 

20 

1,349 

2,698 

,047 

5,397 

6,746 

8,095 

9,444 

10,  793 

12,  142 

5.8 

24 

12.0 

87 

21 

1,351 

2,702 

,062 

5,403 

6,754 

8,105 

9,455 

10,806 

12,  157 

6.0 

25 

12.1 

89 

-22 

1,352 

2,705 

,057 

5,410 

6,762 

8,114 

9,467 

10,  819 

12,  172 

6.1 

26 

12.2 

90 

23 

1,354 

2,708 

,062 

5,416 

6,770 

8,124 

9,478 

10,  832 

12,186 

6.3 

27 

12.3 

91 

24 

1,356 

2,711 

,067 

5,423 

6,778 

8,134 

9,490 

10,845 

12.201 

6.4 

28 

12.4 

.   93 

26 

1,357 

2,715  1     ,072 

5,429 

6,787 

8,144 

9,501 

10,859 

12,  216 

6.5 

29 

12.5 

94 

26 

1,359 

2,718       ,077 

5,436 

6,795 

8,154 

9,513 

10,  872 

12,  231 

6.7 

30 

12.6 

96 

27 

1,361 

2,  721       ,  082 

5.442 

6,803 

8,164 

9,524 

10,885 

12,  245 

6.8 

31 

12.7 

97 

28 

1,362 

2,724 

,087     5,449 

6,811 

8,173 

9,536 

10,898 

12,260 

6.9. 

32 

12.8 

99 

29 

1,364 

2,728 

,092     5,  455 

6,819 

8,183 

9,547 

10,911 

12,  275 

7.0 

33 

12.9 

100 

30 

1,366 

2,731 

,097 

5,462 

6,828 

8,193 

9,559 

10,  924 

12,290 

7.2 

34 

13.0 

102 

31 

1,367 

2,734 

,101 

5,  469 

6,836 

8,203 

9,570 

10,  937 

12,  304 

7.3 

35 

13.1 

103 

32 

1,369 

2,738 

,106  1  5,475 

6,844 

8,213 

9,581 

10,950 

12,  319 

7.4 

36 

13.2 

105 

33 

1,370 

2,741 

,111  i  5,482 

6,852 

8,223 

9,593 

10,963 

12,  334 

7.5 

37 

13.3 

106 

34 

1,372 

2,744 

,116  I  5,488 

6,860 

8,  232 

9,604 

10,  976 

12,  349 

7.6 

38 

13.4 

108 

36     1,374 

2,747 

,121  !  5.495 

6,868 

8,242 

9,616 

10,990 

12,  363 

7.8 

39 

13.5 

109 

36 

1,375 

2,751 

,126 

5,501 

6,877 

8,252 

9,  627 

11,003 

12.  378 

7.9 

40 

13.6 

111 

37 

1,377 

2,754 

,131 

5,508 

6,885 

8,262 

9,639 

11,016 

12,  393 

8.0 

41 

13.7 

112 

38  !  1,379 

2,757 

,136 

5,514 

6,893 

8,272 

9,650 

11,029 

12,  408 

8.1 

42 

13.8 

114 

39     1,380 

2,761 

,141 

5,521 

6,901 

8,282 

9,662 

11,042 

12,  422 

8.2 

43 

13.9 

115 

40     1,382 

2,764 

,146 

5,528 

6,910 

8,291 

9,673 

11,055 

12,437 

8.3 

44 

14.0 

117 

41     1,384 

2,767 

,151 

5,534 

6,918 

8,301 

9,685 

11,068 

12,  452 

8.4 

45 

14.1 

119 

42     1,386 

2,770 

;156 

5,541 

6,926 

8,311 

9,696 

11,081 

12,  467 

8.5 

46 

14.2 

120 

43     1.387 

2,774 

,160 

5,547 

6,934 

8,321 

9,708 

11,095 

12,  481 

8.6 

47 

14.3 

122 

44 

1,388 

2,777 

,165 

5,554 

6,942 

8,331 

9.719 

11,108 

12,  496 

8.7 

48 

14.4 

124 

45 

1,390 

2,780 

,170 

5,560 

6,951 

8,341 

9,731 

11,121 

12,511 

8.8 

49 

14.5 

125 

46 

1,392 

2,784 

,175 

5,  .567 

6,959 

8,351 

9,742 

11,134 

12,  526 

8.9 

50 

14.6 

127 

47 

1,393 

2,787 

4,180 

5,574 

6,967 

8,360 

9,754 

11,  147 

12,  541 

9.0 

51 

14.7 

129 

48 

1,395 

2,790 

4,185 

5,580 

6,975 

8,370 

9,765 

11,160 

12,555 

9.1 

52 

14.8 

130 

19 

1,397 

2,793 

4,190 

5,587 

6,983 

8,380 

9,777 

11,173 

12,  570 

9.2 

53 

14.9 

132 

50 

1,398 

2,797 

4,195 

5,  593 

6,992 

8,390 

9,788 

11,187 

12,  585 

9.3 

54 

15.0 

134 

51 

1,400 

2,800 

4,200 

5,600 

7,000 

8,400 

9,800 

11,200 

12,600 

9.4 

55 

15.1 

135 

52 

1,402 

2,803 

4,205  i  5,606 

7,008 

8,410 

9,811 

11,213 

12,  615 

9.5 

56 

15.2 

137 

53 

1,403 

2,807 

4,210 

5,  613 

7,016 

8,420 

9,823 

11,226 

12,  629 

9.6 

58 

15.3 

139 

54 

1,405 

2,810 

4,215 

5,620 

7,024 

8,429 

9,834 

11,239 

12,644 

9.7 

59 

15.4 

141 

55 

1,407 

2,813 

4,220 

5,626 

7,033 

8,439 

9,8i6 

Il,2o2 

12,  659 

9.8 

60 

15.5 

142 

56 

1,408 

2,816 

4.225 

5,633 

7,041 

8,449 

9,  8o7 

Il,2h6 

12,  674 

9.9 

61 

15.6 

144 

57 

1,410 

2,820 

4,230 

5,639 

7,049 

8,459 

9,869 

11,T9 

12,689 

10.0 

62 

15.7 

146 

58 

1,411 

2,823 

4,234 

5,646 

7,057 

8,465 

9,880 

11,  292 

12,  703 

10.1 

63 

15.8 

148 

59 

1,413 

2,826 

4,239 

5,653 

7,066 

8,479 

9,892 

11,  305 

12,  718 

15.9 

1.50 

16.0 

151 

60 

1,415 

2,830 

4,244 

5,659 

7,074 

8,489 

9,903 

11,318 

12,733 

a  For  all  distances  under  1.6  miles  the  correction  may  be  taken  as  +  5  feet.    Height  of  instrument 
is  assumed  4.5  feet. 


46061—08- 


-19 


290  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  28. — HORIZONTAL  DISTANCES  AND  ELEVATIONS  FROM  STADIA  READINGS. 

This  is  a  most  generally  useful  stadia  table  for  rods  reading  1  foot  to 
the  100  feet  and  with  angles  up  to  30°.  The  values  of  other  measures 
than  those  given  in  the  table  are  obtained  by  multiplying  the  quanti- 
ties under  the  proper  vertical  angle  by  stadia  readings  in  hundreds  of 
units.  The  quantity  representing  the  focal  distance  is  very  small  and 
is  given  at  the  bottom  of  each  page  for  focal  lengths  between  three- 
fourths  and  1-f  feet  and  is  represented  as  a  constant  equal  to  c. 
For  ordinary  work  it  is  not  necessary  to  take  the  latter  into  account. 
The  direct  use  of  the  table  involves  a  multiplication  for  each  result 
obtained. 

Example. — Let  rod  intercept  be  3.25  feet,  and  the  angle  of  inclina- 
tion be  5°  35'.  Then  the  distance  on  the  horizontal  would  be 

^=325  feet. 

If  we  accept  the  focal  distance  /*+  c  as  1.25  feet,  we  have  from  the 
tables 

<Z'  =  3.25  feetX  99.05+1.24=323.15  feet, 
and 

.A=3.25  feetx 9.68+0.11  =  31.57  feet. 


GEOGRAPHIC   TABLES    AND    FORMULAS.  291 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings. 


0°. 

1°. 

2° 

3°. 

Minutes.       Horizon. 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

t&l  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tance. 

tion. 

tance. 

tion. 

tance. 

tion. 

tance. 

tion. 

0 

100.00 

0.00 

99.97 

1.74 

99.88 

3.49 

99.73 

5.23 

2 

100.00 

0.06 

99.97 

1.80 

99.87 

3.55 

99.72 

5.28 

4 

100.00  !       0.12 

99.97 

1.86 

99.87 

3.60 

99.71 

5.34 

6 

100.00         0.17 

99.96 

1.92 

99.87 

3.66 

99.71 

5.40 

8           100.00 

0.23 

99.96 

1.98 

99.86 

3.72 

99.70 

5.46 

10           100.00 

0.29 

99.96 

2.04 

99.86 

3.78 

99.69 

5.52 

12 

100.00 

0.35 

99.96 

2.09 

99.85 

3.84 

99.69 

5.57 

14           100.  00 

0.41 

99.95 

2.15 

99.85 

3.  90       99.  68 

5.63 

16           100.  00 

0.47 

99.95 

2.21 

99.84 

3.  95       99.  68 

5.69 

18           100.  00 

0.52 

99.95 

2.27 

99.84 

4.01 

99.67 

5.75 

20           100.  00 

0.58 

99.95 

2.33 

99.83 

4.07 

99.66. 

5.80 

22           100.  00 

0.64 

99.94 

2.38 

99.83 

4.13 

99.66 

5.86 

24           100.  00 

0.70 

99.94 

2.44 

99.82 

4.18 

99.65 

5.92 

26             99.  99 

0.76 

99.94 

2.50 

99.82 

4.24 

99.64 

5.98 

28             99.  99 

0.81 

99.93 

2.56 

99.81 

4.30 

99.63 

6.04 

30             99.  99 

0.87 

99.93 

2.62 

99.81 

4.36 

99.63 

6.09 

32 

99.99 

0.93 

99.93  ;      2.67 

99.80 

4.42 

99.62 

6.15 

34        ;     99.  99 

0.99 

99.  93         2.  73 

99.80 

4.48 

99.62 

6.21 

36        1     99.99 

1.05 

99.  92         2.  79 

99.79 

4.53 

99.  61 

6.27 

38             99.  99 

1.11 

99.92 

2.85 

99.79 

4.59 

99.60 

6.33 

40             99.  99 

1.16 

99.92 

2.91 

99.78 

4.65 

99.59 

6.38 

42 

99.99 

1.22 

99.91 

2.97 

99.78 

4.71 

99.59 

6.44 

44 

99.98 

1.28 

99.91 

3.02       99.77 

4.76 

99.58 

6.50 

46 

99.98 

1.34 

99.90 

3.  08       99.  77 

4.82 

99.57 

6.56 

48 

99.98 

1.40 

90.90         3.14 

99.76 

4.88 

99.56 

6.61 

50 

99.98 

1.45 

99.90 

3.20 

99.76 

4.94 

99.56 

6.67 

52 

99.98 

1.51 

99.89 

3.26 

99.75 

4.99 

99.55 

6.73 

54 

99.98 

1.57 

99.89 

3.31 

99.74 

5.05 

99.54 

6.78 

56            99.  97 

1.63 

99.89 

3.37 

99.74 

5.11 

99.53 

6.84 

58        I    99.97 

1.69 

99.88 

3.43 

99.73 

5.17 

99.52 

9.90 

60        |    99.97         1.74 

99.88 

3.49 

99.  73 

5.23 

99.51 

6.96 

c=0.  75 

0.  75         0.  01 

'0.75 

0.02 

0.75 

0.03 

0.75 

0.05 

c=1.00         1.00 

0.01 

1.00 

0.03 

1.00 

0.04 

1.00 

0.  06 

c=1.25         1.25         0.02 

1.25 

0.03 

1.25 

0.  05         1.  25 

0.08 

292          GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


4 

3 

5C 

6< 

3 

7 

0^ 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

0 

99.51 

6.96 

99.24 

8.68 

98.91 

10.40 

98.51 

12.10 

2 

99.51 

7.02 

99.23 

8.74 

98.90 

10.45 

98.50 

12.  15 

4 

99.50 

7.07 

99.22 

8.80 

98.88 

10.51 

98.48 

12.21 

6 

99.49 

7.13 

99.21 

8.85 

98.87 

10.57 

98.47 

12.26 

8 

99.48 

7.19 

99.20 

8.91 

98.86 

10.62 

98.46 

12.32 

10 

99.  47' 

7.25 

99.19 

8.97 

98.85 

10.68 

98.44 

12.38 

12 

99.46 

7.30 

99.18 

9.03 

98.83 

10.74 

98.43 

12.43 

14 

99.46 

7.36 

99.17 

9.08 

98.82 

10.79 

98.41 

12.49 

16 

99.45 

7.42 

99.16 

9.14 

98.81 

10.85 

98.40 

12.55 

18 

99.44 

7.48 

99.15 

9.20 

98.80 

10.91 

98.39 

12.60 

20 

99.43 

7.53 

99.14 

9.25 

98.78 

10.96 

98.  37 

12.66 

22 

99.42 

7.59 

99.13 

9.31 

98.77 

11.02 

98.  36 

12.72 

24 

99.41 

7.65 

99.11 

9.37 

98.76 

11.08' 

98.34 

12.77 

26 

99.40 

7.71 

99.10 

9.43 

98.74 

11.13 

98.33 

12.83 

28 

99.  39 

7.76 

99.09 

9.48 

98.73 

11.19 

98.31 

12.88 

30 

99.38 

7.82 

99.08 

9.54 

98.72 

11.25 

98.29 

12.94 

32 

99.33 

7.88 

99.07 

9.60 

98.71 

11.30 

98.28 

13.00 

34 

99.37 

7.94 

99.06 

9.65 

98.69 

11.36 

98.27 

13.05 

36 

99.36 

7.99 

99.05 

9.71 

98.68 

11.  42 

98.25 

13.11 

38 

99.35 

8.05 

99.04 

9.77 

98.67 

11.47 

98.24 

13.17 

40 

99.34 

8.11 

99.03 

9.83 

98.65 

11.53 

98.22 

13.22 

42 

99.33 

8.17 

.  99.  01 

9.88 

98.64 

11.59 

98.20 

13.28 

44 

99.32 

8.22 

99.00 

9.94 

98.63 

11.64 

98.19 

13.33 

46 

99.  31 

8.28 

98.99 

10.00 

98.61 

11.70 

98.17 

13.39 

48 

99.30 

8.34 

98.98 

10.05 

98.60 

11.76 

98.16 

13.45 

50 

99.29 

8.40 

98.97 

10.11 

98.58 

11.81 

98.14 

13.50 

52 

99.28 

8.45 

98.96 

10.17 

98.57 

11.87 

98.13 

13.56 

54 

99.27 

8.51 

98.94 

10.22 

98.56 

11.93 

98.11 

13.61 

56 

99.26 

8.57 

98.93 

10.28 

98.54 

11.98 

98.10 

13.67 

58 

99.  25 

8.63 

98.92 

10.34 

98.  53 

12.04 

98.08 

13.73 

60. 

99.24 

8.68 

98.91 

-10.40 

98.51 

12.10 

98.06 

13.78 

c=0.  75 

0.75 

0.06 

0.75 

0.07 

0.75 

0.08 

0.74 

0.10 

c=1.00 

1.00 

0.08 

0.99 

0.09 

0.99 

0.11 

0.99 

0.13 

c=1.25 

1.25 

0.10 

1.24 

0.11 

1.24 

0.14 

1.24 

0.16 

QEOGKAPHIC    TABLES    AND    FORMULAS.  293 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


8°. 

9°. 

10°. 

11°. 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

0 

98.06 

13.78 

97.55 

15.45 

96.98 

17.10 

96.36 

18.73 

2 

98.05 

13.84 

97.53 

15.51 

96.96 

17.16 

96.34 

18.78 

4 

98.03 

13.89 

97.52 

15.56 

96.94 

17.21 

96.32 

18.84 

6 

98.01 

13.95 

97.50 

15.62 

96.92 

17.26 

96.29 

18.89 

8 

98.00 

14.01 

97.48 

15.  67 

96.90 

17.32 

96.27 

18.95 

10 

97.98 

14.06 

97.46 

15.73 

96.88 

17.37 

96.25 

19.00 

12 

97.97 

14.12 

97.44 

15.78 

96.86 

17.43 

96.23 

19.05 

14 

97.95 

14.17 

97.43 

15.84 

96.84 

17.48 

96.21 

19.11 

16 

97.  93 

14.23 

97.41 

15.89 

96.82 

17.54 

96.18 

19.16 

18 

97.92 

14.28 

97.39 

15.95 

96.80 

17.59 

96.16 

19.21 

20 

97.90 

14.34 

97.37 

16.00 

96.78 

17.65 

96.14 

19.27 

22 

97.88 

14.40 

97.35 

16.06 

96.76 

17.70 

96.12 

19.32 

24 

97.87 

14.45 

97.33 

16.  11 

96.74 

17.76 

96.09 

19.38 

26 

97.85 

14.51 

97.31 

16.17 

96.72 

17.81 

96.07 

19.43 

28 

97.83 

14.56 

97,29 

16.22 

96.  70 

17.86 

96.05 

19.48 

30 

97.82 

14.62 

97.28 

16.28 

96.68 

17.92 

96.  03 

19.54 

32 

97.80 

14.67 

97.26 

16.33 

96.66 

17.97 

96.00 

19.59 

34 

97.78 

14.  73 

97.24 

16.39 

96.64 

18.03 

95.98 

19.64 

36 

97.76 

14.79 

97.22 

16.44 

96.62 

18.08 

95.96 

19.70 

38 

97.75 

14.84 

97.20 

16.50 

96.60 

18.14 

95.93 

19.75 

40 

97.73 

14.90 

97.18 

16.55 

96.  57 

18.19 

95.91 

19.80 

42 

97.71 

14.95 

97.16 

16.61 

96.55 

18.24 

95.89 

19.86 

44 

97.69 

15.01 

97.14 

16.66 

96.53 

18.30 

95.86 

19.91 

46 

97.68 

15.06 

97.12 

16.72 

96.  51 

18.35 

95.84 

19.96 

48 

97.66 

15.12 

97.10 

16.77 

96.49 

18.41 

95.82 

20.02 

50 

97.64 

15.17 

97.08 

16.83 

96.47 

18.46 

95.79 

20.07 

52 

97.62 

15.23 

97.06 

16.88 

96.45 

18.51 

95.77 

20.12 

54 

97.61 

15.28 

97.04 

16.94 

96.42 

18.57 

95.75 

20.18 

56 

97.59 

15.34 

97.02 

16.99 

96.40 

18.  62 

95.72 

20.23 

58 

97.57 

15.40 

97.00 

17.05 

96.38 

18.68 

95.70 

20.28 

60 

97.55 

15.45 

96.98 

17.10 

96.36 

18.73 

95.68 

20.34 

c=0.  75 

0.74 

0.11 

0.74 

0.12 

0.74         0.14 

0.73 

0.15 

c=1.00 

0.99 

0.15 

0.99 

0.16 

0.98 

0.18 

0.98 

0.20 

c=l.  25 

1.23 

0.18 

1.23 

0.21 

1.23 

0.23 

1.22 

0.25 

294  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


12°. 

13°. 

14°. 

15°. 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

0 

95.68 

20.34 

94.94 

21.92 

94.  15 

23.47 

93.30 

25.00 

2 

95.65 

20.39 

94.91 

21.97 

94.12 

23.52 

93.27 

25.05 

4 

95.63 

20.44 

94.89 

22.02 

94.09 

23.58 

93.24 

25.10 

6 

95.61 

20.50 

94.86 

22.08 

94.07 

23.63 

93.21 

25.15 

8 

95.58 

20.  55 

94.84 

22.13 

94.04 

23.68 

93.18 

25.20 

10 

95.56 

20.60 

94.  81 

22.18 

94.01 

23.73 

93.16 

25.25 

12 

95.53 

20.66 

94.79 

22.23 

93.98 

23.78 

93.13 

25.30 

14 

95.51 

20.71 

94.76 

22.28 

93.95 

23.83 

93.10 

25.35 

16 

95.49 

20.76 

94.73 

22.34 

93.93 

23.88 

93.07 

25.40 

18 

95.46 

20  81 

94.71 

22.39 

93.90 

23.  93 

93.04 

25.45 

20 

95.44 

20.87 

94.68 

22.44 

93.87 

23.99 

93.01 

25.50 

22 

95.41 

20.92 

94.66 

22.49 

93.84 

24.04 

92.98 

25.55 

24 

95.39 

20.97 

94.63 

22.54 

93.81 

24.09 

92.95 

25.60 

26 

95.36 

21.  03 

94.60 

22.60 

93.79 

24.14 

92.92 

25.65 

28 

95.34 

21.08 

94.58 

22.65 

93.76 

24.19 

92.89 

25.70 

30 

95.32 

21.13 

94.55 

22.70 

93.73 

24.24 

92.86 

25.75 

32 

95.29 

21.18 

94.52 

22.75 

93.  70 

24.29 

92.83 

25.80 

34 

95.27 

21.24 

94.50 

22.80 

93.67 

24.34 

92.80 

25.85 

36 

95.24 

21.29 

94.47 

22.85 

93.65 

24.39 

92.77 

25.90 

38 

95.22 

21.34 

94.44 

22.91 

93.62 

24.44 

92.74 

25.95 

40 

95.19 

21.39 

94.42 

22.96 

93.  59 

24.49 

92.71 

26.00 

42 

95.17 

21.45 

94.39 

23.01 

93.56 

24.55 

92.68 

26.05 

44 

95.14 

21.50 

94.36 

23.06 

93.  53 

24.60 

92.65 

26.10 

46 

95.12 

21.55 

94.34 

23.11 

93.50 

24.65 

92.62 

26.15 

48 

95.09 

21.60 

94.31 

23.  16 

93.47 

24.70 

92.59 

26.20 

50 

95.07 

21.66 

94.28 

23.  22 

93.45 

24.75 

92.56 

26.25 

52 

95.04 

21.71 

94.26 

23.27 

93.42 

24.80 

92.53 

26.30 

54 

95.02 

21.76 

94.23 

23.32 

93.39 

24.85 

92.49 

26.35 

56 

94.99 

21.81 

94.20 

23.  37 

93.36 

24.90 

92.46 

26.40 

58 

94.97 

21.87 

94.17 

23.42 

93.33 

24.  95 

92.43 

26.45 

60 

94.94 

21.92 

94.  15 

23.47 

93.30 

25.00 

92.40 

26.  50 

c=0.  75 

0.73 

0.16 

0.73 

0.17 

0.73 

0.19 

0.72 

0.20 

c=1.00 

0.98 

0.22 

0.97 

0.23 

0.97 

0.25 

0.96 

0.27 

c=1.25 

1.22 

0.27 

1.21 

0.29 

1.21 

0.31 

1.20 

0.34 

GEOGRAPHIC    TABLES   AND    FORMULAS.  295 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


16°. 

17=. 

18°. 

19°. 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

•    tion. 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

0 

92.40 

26.50 

91.45 

27.96 

90.45 

29.39 

89.40 

30.  78 

2 

92.37 

26.55 

91.42 

28.01 

90.42 

29.44 

89.36 

30.  83 

4 

92.34 

26.59 

91.39 

28.06 

90.38 

29.48 

89.  33 

30.87 

6 

92.31 

26.64 

91.35 

28.10 

90.35 

29.53 

89.29 

30.  92 

8 

92.28 

26.69 

91.32 

28.15 

90.31 

29.58 

89.26 

30.97 

10 

92.25 

26.74 

91.29 

28.20 

90.28 

29.62 

89.22 

31.01 

12 

92.22 

26.79 

91.26 

28.25 

90.24 

29.67 

89.18 

31.06 

14 

92.19 

26.84 

91.22 

28.30 

90.21 

29.72 

89.15 

31.10 

16 

92.15 

26.89 

91.  19 

28.34 

90.18 

29.76 

89.11 

31.15 

18 

92.12 

26.94 

91.16 

28.39 

90.14 

29.81 

89.08 

31.19 

20 

92.09 

26.99 

91.12 

28.44 

90.11 

29.86 

89.04 

31.24 

22 

92.06 

27.04 

91.09 

28.49 

90.07 

29.90 

89.00 

31.28 

24 

92.03 

27.09 

91.06 

28.54 

90.04 

29.95 

88.96 

31.33 

26 

92.00 

27.13 

91.02 

28.58 

90.00 

30.00 

88.93 

31.38 

28 

91.97 

27.18 

90.99 

28.63 

89.97 

30.04 

88.89 

31.42 

30 

91.93 

27.23 

90.96 

28.68 

89.93 

30.  09 

88.86 

31.47 

32 

91.90 

27.28 

90.92 

28.73 

89.90 

30.14 

88.82 

31.51 

34 

91.87 

27.33 

90.89 

28.77 

89.86 

30.  19 

88.78 

31.56 

36 

91.84 

27.  38 

90.86 

28.82 

89.83 

30.  23 

88.75 

31.60 

38 

91.81 

27.43 

90.82 

28.87 

89.79 

30.28 

88.71 

31.65 

40 

91.77 

27.48 

90.79 

28.92 

89.76 

30.  32 

88.67 

31.69 

42 

91.74 

27.52 

90.76 

28.96 

89.72 

30.  37 

88.64 

31.74 

44 

91.71 

27.57 

90.72 

29.01 

89.69 

30.41 

88.60 

31.78 

46 

91.68 

27.62 

90.69 

29.06 

89.65 

30.46 

88.56 

31.83 

48 

91.65 

27.67 

90.66 

29.11 

89.61 

30.51 

88.  53 

31.87 

50 

91.61 

27.72 

90.62 

29.15 

89.  58 

30.  55 

88.49 

31.92 

52 

91.58 

27.77 

90.59 

29.20 

89.54 

30.  60 

88.45 

31.96 

54 

91.  55 

27.81 

90.  55 

29.25 

89.51 

30.65 

88.41 

32.  01 

56 

91.52 

27.86 

90.52 

29.30 

89.47 

30.69 

88.38 

32.05 

58 

91.48 

27.91 

90.48 

29.34 

89.44 

30.74 

88.34 

32.09 

60 

91.45 

27.96 

90.  45 

29.39 

89.40 

30.78 

88.  30 

32.14 

c=0.  75 

0.72 

0.21 

0.72 

0.23 

0.71 

0.24 

0.71 

0.25 

c=1.00 

0.86 

0.28 

0.95 

0.30 

0.95 

0.32 

0.94 

0.33 

c=l.  25 

1.20 

0.35 

1.19 

0.38 

1.19 

0.40 

1.18 

0.42 

296  GEOGRAPHIC   TABLES    AND    FORMULAS. 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


20°. 

21°. 

22°. 

23°. 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

0 

88.30 

32.14 

87.16 

33.46 

85.97 

34.73 

84.73 

35.97 

2 

88.26 

32.18 

87.12 

33.50 

85.93 

34.77 

84.69 

36.01 

4 

88.23 

32.23 

87.08 

33.54 

85.89 

34.82 

84.65 

36.05 

6 

88.19 

32.27 

87.04 

33.59 

85.85 

34.86 

84.61 

36.09 

8 

88.15 

32.32 

87.00 

33.63 

85.80 

34.90 

84.57 

36.  13 

10 

88.11 

32.36 

86.96 

33.67 

85.76 

34.94 

84.52 

36.17 

12 

88.08 

32.41 

86.92 

33.72 

85.72 

34.98 

84.48 

36.21 

14 

88.04 

32.45 

86.88 

33.76 

85.68 

35.02 

84.44 

36.25 

16 

88.00 

32.49 

86.84 

33.80 

85.64 

35.07 

84.40 

36.29 

18 

87.96 

32.54 

86.80 

33.84 

85.60 

35.11 

84.35 

36.33  " 

20 

87.93 

32.  58 

86.77 

33.89 

85.56 

35.15 

84.31 

36.37 

22 

87.89 

32.63 

86.73 

33.93 

85.52 

35.19 

84.27 

36.41 

24 

87.85 

32.67 

86.69 

33.97 

85.48 

35.23 

84.23 

36.45 

26 

87.81 

32.72 

86.65 

34.01 

85.44 

35.27 

84.18 

36.49 

28 

87.77 

32.76 

86.61 

34.06 

85.40 

35.31 

84.14 

36.  53 

30 

87.74 

32.  80 

86.57 

34.10 

85.36 

35.  36 

84.10 

36.  57 

32 

87.70 

32.85 

86.53 

34.14 

85.31 

35.  40 

84.06 

36.61 

34 

87.66 

32.89 

86.49 

34.18 

85.27 

35.44 

84.01 

36.  65 

36 

•  87.  62 

32.  93 

86.45 

34.23 

85.23 

35.  48 

83.97 

36.69 

38 

87.58 

32.98 

86.41 

34.27 

85.19 

35.52 

83.93 

36.  73 

40 

87.54 

33.  02 

86.37 

34.31 

85.15 

35.56 

83.89 

36.77 

42 

87.51 

33.07 

86.33 

34.35 

85.11 

35.60 

83.84 

36.80 

44 

87.47 

33.11 

86.29 

34.40 

85.07 

35.64 

83.80 

36.84 

46 

87.43 

33.15 

86.25 

34.44 

85.02 

35.68 

83.76 

36.  88 

48 

87.39 

33.20 

86:21 

34.48 

84.98 

35.72 

83.72 

36.92 

50 

87.35 

33.24 

86.17 

34.52 

84.94 

35.76 

83.67 

36.96 

52 

87.31 

33.  28 

86.13 

34.57 

84.90 

35.80 

83.63 

37.00 

54 

87.27 

33.33 

86.09 

34.  61 

84.86 

35.85 

83.59 

37.04 

56 

87.24 

33.37 

86.05 

34.65 

84.82 

35.89 

83.54 

37.  08 

58 

87.20 

33.41 

86.01 

34.69 

84.77 

35.93 

83.50 

37.12 

60 

87.16 

33.46 

85.97 

34.  73 

84.73 

35.97 

83.46 

37.16 

c=0.  75 

0.70 

0.26 

0.70 

0.27 

0.69 

0.29 

0.69 

0.30 

r=1.00 

0.94 

0.35 

0.93 

0.37 

0.92 

0.38 

0.92 

0.40 

c=1.25 

1.17 

0.44 

1.16 

0.46 

1.15 

0.48 

1.15 

0.50 

GEOGRAPHIC   TABLES   ATSTD   FORMULAS.  297 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


24°. 

25°. 

26°. 

27°. 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

tances. 

tion. 

0 

83.46 

37.16 

82.14 

38.30 

80.78 

39.40 

79.39 

40.45 

2 

83.41 

37.20 

82.09 

38.34 

80.74 

39.44 

79.34 

40.49 

4 

83.37 

37.23 

82.05 

38.38 

80.69 

39.47 

79.30 

40.52 

6 

83.33 

37.27 

82.01 

38.41 

80.65 

39.51 

79.25 

40.55 

8 

83.28 

37.31 

81.96 

38.45 

80.60 

39.54 

79.20 

40.59 

10 

83.24 

37.35 

81.92 

38.49 

80.55 

39.58 

79.15 

40.62 

12 

83.20 

37.39 

81.87 

38.53 

80.51 

39.61 

79.11 

40.66 

14 

83.15 

37.43 

81.83 

38.56 

80.46 

39.65 

79.06 

40.69 

16 

83.11 

37.47 

81/78 

38.60 

80.41 

39.69 

79.01 

40.72 

18 

83.07 

37.51 

81.74 

38.64 

80.37 

39.72 

78.  96 

40.76 

20 

83.02 

37.54 

81.69 

38.67 

80.32 

39.76 

78.92 

40.79 

22 

82.98 

37.58 

81.65 

38.71 

80.28 

39.79 

78.87 

40.82 

24 

82.93 

37.62 

81.60 

38.75 

80.23 

39,83 

78.82 

40.86 

26 

82.89 

37.66 

81.56 

38.78 

80.18 

39.86 

78.77 

40.89 

28 

82.85 

37.70 

81.51 

38.62 

80.14 

39.90 

78.73 

40.92 

30 

82.80 

37.74 

81.47 

38.86 

80.09 

39.93 

78.68 

40.96 

32 

82.76 

37.77 

81.42 

38.89 

80.04 

39.97 

78.63 

40.99 

34 

82.72 

37.81 

81.38 

38.93 

80.00 

40.00 

78.58 

41.02 

36 

82.67 

37.85 

81.33 

38.97 

79.95 

40.04 

78.54 

41.06 

38 

82.63 

37.89 

81.28 

39.00 

79.90 

40.07 

78.49 

41.09 

40 

82.58 

37.93 

81.24 

39.04 

79.86 

40.11 

78.44 

41.12 

42 

82.54 

37.96 

81.19 

39.08 

79.81 

40.14 

78.39 

41.16 

44 

82.49 

38.00 

81.15 

39.11 

79.76 

40.18 

78.34 

41.19 

46 

82.45 

38.04 

81.10 

39.15 

79.72 

40.21 

78.30 

41.22 

43 

82.41 

38.08 

81.06 

39.18 

79.67 

40.24 

78.25 

41.26 

50 

82.36 

38.11 

81.01 

39.22 

79.62 

40.28 

78.20 

41.29 

52 

82.32 

38.15 

80.97 

39.26 

79.58 

40.31 

78.15 

41.32 

54 

82.27 

38.19 

80.92 

39.29 

79.53 

40.35 

78.10 

41.35 

56 

82.23 

38.23 

80.87 

39.33 

79.48 

40.38 

78.06 

41.39 

58             82.  18 

38.26 

80.83 

39.36 

79.44 

40.42 

78.  01 

41.42 

60 

82.14 

38.30 

80.78 

39.40 

79.39 

40.45 

77.96 

41.45  ' 

c=0.  75 

0.68 

0.31 

0.68 

0.32 

0.67 

0.33 

0.66 

0.35 

c=1.00 

0.91 

0.41 

0.90 

0.43 

0.89 

0.45 

0.89 

0.46 

c=1.25 

1.14 

0.52 

1.13 

0.54 

1.12 

0.56 

1.11 

0.58 

298  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  28. — Horizontal  distances  and  elevations  from  stadia  readings — Continued. 


28°. 

29°. 

30°. 

Minutes. 

Horizon- 

Difference 

Horizon- 

Difference 

Horizon- 

Difference 

tal  dis- 

of eleva- 

tal dis- 

of eleva- 

tal dis- 

of eleva- 

tances. 

tions. 

tances. 

tions. 

tances. 

tions. 

0 

77.96 

41.45 

76.  50 

42.40 

75.00 

43.30 

2 

77.91 

41.48 

76.45 

42.43 

74.95 

43.33 

4 

77.86 

41.52 

76.40 

42.46 

74.90 

43.36 

6 

77.81 

41.55 

76.35 

42.49 

74.85 

43.39 

8 

77.77 

41.58 

76.30 

42.53 

74.80 

43.42 

10 

77.72 

41.61 

76.25 

42.56 

74.75 

43.45 

12 

77.67 

41.65 

76.20 

42.59 

74.70 

43.47 

14 

77.62 

41.68 

76.15 

.42.  62 

74.65 

43.50 

16 

77.57 

41.71 

76.10 

42.65 

74.60 

43.53 

18 

77.52 

41.74 

76.05 

42.68 

74.55 

43.56 

20 

77.48 

41.77 

76.00 

42.71 

74.49 

43.59 

22 

77.42 

41.81 

75.95 

42.74 

74.44 

43.62 

24 

77.38 

41.84 

75.90 

42.77 

74.39 

43.65 

26 

77.33 

41.87 

75.85 

42.80 

74.34 

43.67 

28 

77.28 

41.90 

75.80 

42.83 

74.29 

43.70 

30 

77.23 

41.93 

75.75 

42.86 

74.24 

43.73 

32 

77.18 

41.97 

75.70 

42.  89 

74.19 

43.76 

34 

77.13 

42.00 

75.65 

42.92 

74.14 

43.79 

36 

77.09 

42.03 

75.60 

42.95 

74.09 

43.82 

38 

77.04 

42.06 

75.55 

42.98 

74.  04 

43.84 

40 

76.99 

42.09 

75.50 

43.01 

73.99 

43.87 

42 

76.94 

42.12 

75.45 

43.  04 

73.93 

43.90 

44 

76.89 

42.  15 

75.40 

43.07 

73.88 

43.93 

46 

76.84 

42.19 

73.35 

43.10 

73.83 

43.95 

48 

76.79 

42.22 

75.30 

43.13 

73.78 

43.98 

50 

76.74 

42.  25 

75.25 

43.16 

73.73 

44.01 

52 

76.69 

42.28 

75.20 

43.18 

73.68 

44.04 

54 

76.64 

42.  31 

75.15 

43.21 

73.63 

44.07 

56 

76.59 

42.34 

75.10 

43.24 

73.58 

44.09 

58 

76.55 

42.37 

75.  05 

43.27 

73.52 

44.12 

60 

76.50 

42.40 

75.00 

43.30 

73.47 

44.15 

c=0.  75 

0.66 

0.36 

0.65 

0.37 

0.65 

0.38 

c=1.00 

0.88 

0.48 

0.87 

0.49 

0.86 

0.51 

c=l.  25 

1.10 

0.60 

1.09 

0.62 

1.08 

0.64 

GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  29. — For  converting  metric  into  United  States  measures. 
LINEAR 


299 


Meters.       Inches. 

Meters.         Feet. 

Meters.       Yards. 

Kilo-          Mil  AC 
meters.        Mlles" 

1           39.  3700 

1         3.  280833 

1         1.093611           1          0.62137 

2          78.  7400 

2        6.  561667 

2        2.  187222 

2           1.  24274 

3        118.  1100 

3        9.  842500 

3        3.  280833 

3            .86411 

4        157.  4800 

4       13.  123333 

4         4.  374444 

4           2.  48548 

5        196.  8500 

5       16.  404166 

5        5.  468056 

5          3.  10685 

6        236.  2200 

6      19.  685000 

6        6.561667 

6          3.  72822 

7        275.  5900 

7      22.  965833 

7        7.  655278 

7          4.  34959 

8        314.  9600 

8      26.  246666 

8        8.748889 

8          4.  97096 

9        354.  3300 

9      29.  527500 

9        9.  842500 

9          5.  59233 

SQUARE. 


Scqen«e         **™« 
Srs.         mches' 

Square         Square 
meters.          feet. 

Square         Square 
meters.         yards. 

SSL      A— 

1             0.  1550 

1             10.  764 

1               1.  196 

1              2.  471 

2            0*.  3100 

2            21.528 

2              2.  392 

2              4.  942 

3            0.  4650 

3            32.  292 

3             3.  588 

3              7.413 

4            0.  6200 

4            43.  055 

4              4.  784 

4             9.  884 

5            0.  7750 

5            53.  819 

5             5.  980 

5            12.  355 

6            0.  9300 

6            64.  583 

6              7.  176 

6            14.  826  - 

7            1.  0850 

7            75.  347 

7             8.  372 

7            17.  297 

8            1.  2400 

8            86.  Ill 

8             9.  568 

8            19.  768 

9            1.  3950 

9            96.  875 

9            10.  764 

9            22.  239 

300 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


TABLE  30. — For  converting  United  States  measures  into  metric. 

LINEAR. 


""he,          «L 

Feet.           Meters. 

Yards.        Meters. 

Milps            Kilo- 
les-          meters. 

1          25.  4001 

1         0.  304801 

1      .   0.914402 

1          1.  60935 

2          50.  8001 

2        0.  609601 

2        1.  828804 

2          3.  21869 

3          76.  2002 

3        0.  914402 

3        2.  743205 

3          4.  82804 

4        101.  6002 

4        1.  219202 

4        3.  657607 

4          6.  43739 

5        127.  0003 

5        1.524003 

5        4.  572009 

5          8.  04674 

6        152.  4003 

6        1.828804 

6        5.  486411 

6          9.  65608 

7        177.  8004 

7        2.  133604 

7        6.  400813 

7        11.  26543 

8        203.  2004 

8        2.  438405 

8        7.  315215 

8        12.  87478 

9        228.  6005 

9        2.  743205 

9        8.  229616 

9        14.  48412 

SQUARE. 


^r6        Seqena" 
inches.        meetelrg 

s^uare         SSe 
feet-            meters. 

Square         Square 
yards.        meters. 

Aprp_             Hec- 
tares. 

1               6.  452 

1               9.  290 

1                0.  836 

1             0.4047 

2            12.  903 

2            18.  581 

2              1.  672 

2      .      0.  8094 

3            19.  355 

3            27.  871 

3              2.  508 

3             1.2141 

4            25.807 

4            37.  161 

4              3.344 

4            1.  6187 

5            32.  258 

5            46.  452 

5              4.  181 

5            2.  0234 

6            38.  710 

6            55.  742 

6             5.  017 

6            2.  4281 

7            45.  161 

7            65.  032 

7              5.  853 

7            2.  8328 

8            51.  613 

8            74.  323 

8             6.  689 

8            3.  2375 

9            58.  065 

9            83.  613 

9              7.  525 

9            3.  6422 

GEOGRAPHIC    TABLES    AND    FORMULAS. 


301 


TABLE  31.— FOR   INTEKCONVERSION  OF  MILES  AND  LOGARITHMS  OF  METERS,  FOR  DIS- 
TANCES  FROM   10  TO   100  MILES. 

The  value  adopted  for  the  meter  is  39.3700  inches.  Distances 
between  triangulation  stations  are  given  in  logarithms  of  meters,  but 
for  general  use  distances  in  miles  are  most  frequently  desired. 

The  following  examples  illustrate  use  of  the  table: 

To  find  the  number  of  miles  corresponding  to  log.  distance  in  meters  . . 4.  56857 

Next  lower  log.  in  table  is  for  23.00  miles 4.  56838 


Difference 

Corresponding  to  tabular  difference  for  0.01  mile. 
Hence  distance  required  is  23.01  miles. 


19 


For  distances  less  than  10  miles  proceed  as  above;  first  adding  1  to 
the  characteristic  of  the  given  logarithm  and  afterwards  dividing  the 
corresponding  number  of  miles  by  10.  Example: 

Having  given  the  log.  3.84062,  which  is  less  than  any  given  in 
the  table,  and  therefore  for  a  distance  less  than  10  miles,  adding 
1  to  the  characteristic  of  the  logarithm  gives  4.84062,  which  cor- 
responds to  a  distance  of  43.05  miles.  Hence  the  distance  sought  is 

43.05 

=4.305  miles. 

To  change—  '(Add.) 

Log.  of  miles  to  log.  of  meters f  3.  2066498 

Log.  of  yards  to  log.  of  meters 9. 9611371 

Log.  of  feet  to  log.  of  meters 9. 4840158 

Log.  of  inches  to  log.  of  meters 8.  4048346 

Log.  of  meters  to  log.  of  miles 6.  7933502 

Log.  of  meters  to  log.  of  yards 0. 0388629 

Log.  of  meters  to  log.  of  feet 0.  5159842 

Log.  of  meters  to  log.  of  inches 1.  5951654 

TABLE  31. — For  inttrconversion  of  miles  and  logarithms  of  meters. 
[Prepared  by  S.  S.  Gannett.] 


Miles. 

Log.meter,™- 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

10.00 

4.20665        43 

10.50 

4.  22784 

41 

11.00 

4.  24804 

39 

.05 

4.  20882 

.55 

4.  22990 

.05 

4.  25001 

.10 

4.  21097 

.60 

4.  23196 

.10 

4.  25197 

.15 

4.  21312 

.65 

4.  23400 

.15 

4.  25393 

.20 

4.21525        42 

.70 

4.  23603 

.20 

4.  25587 

.25 

4.21737 

.75 

4.  23806 

40 

.25 

4.  25780 

.30 

4.  21949 

.80 

4.  24007 

.30 

4.  25973 

38 

.35 

4.  22159 

.85 

4.  24208 

.35 

4.  26165 

.40 

4.  22368 

.90 

4.  24408 

.40 

4.  26355 

.45 

4.  22577 

41 

.95 

4.  24606 

.45 

4.  26545 

302  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

11.50 

4.  26735 

38 

14.00 

4.  35278 

31 

16.50 

4.  42413 

26 

.55 

4.  26923 

.05 

4.  35433 

.55 

4.  42545 

.60 

4.27111 

37 

.10 

4.  35587 

.60 

4.  42676 

.65 

4.  27298 

.15 

4.  35741 

.65 

4.  42806 

.70 

4.  27484 

.20 

4.  35894 

.70 

4.  42937 

.75 

4.  27669 

.25 

4.  36047 

30 

.75 

4.  43067 

.80 

4.  27853 

.30 

4.  36199 

.80 

4.  43196 

.85 

4.  28037 

.35 

4.  36350 

.85 

4.  43325 

.90 

4.  28220 

36 

.40 

4.  36501 

.90 

4.  43454 

.95 

4.  28402 

.45 

4.  36652 

.95 

4.  43582 

12.00 

4.  28583 

.50 

4.  36802 

17.00 

4.  43710 

25 

.05 

4.  28764 

.55 

4.  36951 

.05 

4.  43837 

.10 

4.  28944 

.60 

4.37100 

.10 

4.  43964 

.15 

4.  29123 

.65 

4.  37249 

.15 

4.  44091 

.20 

4.  29301 

.70 

4.  37397 

29 

.20 

4.  44218 

.25 

4.  29479 

35 

.75 

4.  37544 

.25 

4.  44344 

.30 

4.  29656 

.80 

4.  37691 

.30 

4.  44470 

.35 

4.  29832 

.85 

4.  37838 

.35 

4.  44595 

.40 

4.  30007 

.90 

4.  37984 

.40 

4.  44720 

.45 

4.  30182 

.95 

4.  38129 

.45 

4.  44845 

.50 

4.  30356 

15.  00 

4.  38274 

.50 

4.  44969 

.55 

4.  30529 

.05 

4.  38419 

.55 

4.  45093 

.60 

4.  30702 

34 

.10 

4.  38563 

.60 

4.  45216 

.65 

4.  30874 

.15 

4.  38706 

.65 

4.  45339 

.70 

4.  31046 

.20 

4.  38849 

.70 

4.  45462 

.75 

4.  31216 

.25 

4.  38992 

28 

.75 

4.  45585 

24 

.80 

4.  31386 

.30 

4.  39134 

.80 

4.  45707 

.85 

4.  31555 

.35 

4.  39276 

.85 

4.45829 

.90 

4.31724 

.40 

4.  39417 

.90 

4.  45950 

.95 

4.  31892 

33 

.45 

4.  39558 

.95 

4.46071 

13.00 

4.  32059 

.50 

4.  39698 

18.00 

4.  46192 

.05 

4.  32226 

.55 

4.  39838 

.05* 

4.  46313 

.10 

4.  32392 

.60 

4.  39977 

.10 

4.  46433 

.15 

4.  32558 

.65 

4.  40116 

.15 

4.  46553 

.20 

4.  32722 

.70 

4.  40255 

.20 

4.  46672 

.25 

4.  32887 

.75 

4.  40393 

.25 

4.  46791 

.30 

4.  33050 

.80 

4.  40531 

27 

.30 

4.  46910 

.35 

4.  33213 

32 

.85 

4.  40668 

.35 

4.  47029 

.40 

4.  33375 

.90 

4.  40805 

.40 

4.  47147 

.45 

4.  33537 

.95 

4.  40941 

.45 

4.  47265 

23 

.50 

4.  33698 

16.00 

4.  41077 

.50 

4.  47382 

.55 

4.  33859 

.05 

4.41213 

.55 

4.  47499 

.60 

4.  34019 

.10 

4.  41348 

.60 

4.  47616 

.65 

4.  34178 

.15 

4.41482 

.65 

4.  47733 

.70 

4.  34337 

.20 

4.  41616 

.70 

4.  47849 

.75 

4.  34495 

.25 

4.  41750 

.75 

4.  47965 

.80 

4.  34653 

31 

.30 

4.  41884 

.80 

•  4.48081 

.85 

4.  34810 

.35 

4.42017 

26 

.85 

4.48196 

.90 

4.  34966 

.40 

4.  42149 

.90 

4.48311 

.95 

4.  35122 

.45 

4.  42282 

.95 

4.  48426 

GEOGRAPHIC    TABLES    AND    FORMULAS.  303 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

19.00 

4.48540 

23 

21.50 

4.  53909 

20 

24.00 

4.  58686 

18 

.05 

4.48654 

.55 

4.  54010 

.05 

4.  58777 

.10 

4.  48768 

.60 

4.54110 

.10 

4.  58867 

.15 

4.  48882 

.65 

4.54211 

.15 

4.  58957 

.20 

4.  48995 

.70 

4.  54311 

.20 

4.  59047 

.25 

4.  49108 

.75 

4.54411 

.25 

4.  59136 

.30 

4.  49221 

22 

.80 

4.  54511 

.30 

4.  59226 

.35 

4.  49333 

.85 

4.  54610 

.35   4.  59315 

.40 

4.  49445 

.90 

4.  54709 

.40 

4.  59404 

.45 

4.  49557 

.95 

4.  54808 

.  45   4.  59493 

.50 

4.49669 

22.00 

4.  54907 

.50 

4.  59582 

.55 

4.  49780 

.05 

4.55006 

.55 

4.  59670 

.60 

4.49891 

.10 

4.  55104 

.60 

4.  59759 

.65 

4.50001 

.15 

4.  55202 

.65 

4.  59847 

.70 

4.  50112 

.20 

4.  55300 

.70 

4.  59935 

.75 

4.  50222 

.25 

4.  55398 

19 

.75 

4.  60023 

.80 

4.50332 

.30 

4.  55495 

.80 

4.  60110 

.85 

4.  50441 

.35 

4.  55593 

.85 

4.  60198 

.90 

4.  50550 

.40 

4.  55690 

.90 

4.  60285 

17 

.95 

4.  50659 

.45 

4.  55787 

.95 

4.  60372 

20.00 

4.  50768 

.50 

4.  55883 

25.00 

4.  60459 

.05 

4.  50876 

.55 

4.  55980 

.05 

4.  60546 

.10 

4.50985 

.60 

4.  56076 

.10 

4.  60632 

.15 

4.51093 

.65 

4.  56172 

.15 

4.  60719 

.20 

4.  51200 

.70 

4.  56268 

.20 

4.  60805 

.25 

4.51308 

21 

.75 

4.  56363 

.25 

4.  60801 

.30 

4.  51415 

.80 

4.  56459 

.30 

4.  60977 

.35 

4.  51521 

.85 

4.56554 

.35 

4.  61063 

.40 

4.  51628 

.90 

4.  56649 

.40 

4.  61148 

.45 

4.  51734 

.95 

4.  56743 

.45 

4.  61234 

.50 

4.  51840 

23.00 

4.  56838 

.50 

4.  61319 

.55 

4.  51946 

.05 

4.  56932 

.55 

4.  61404 

.60 

4.  52052 

.10 

4.  57026 

.60 

4.  61489 

.65 

4.  52157 

.15 

4.  57120 

.65 

4.  61574 

.70 

4.  52262 

.20 

4.  57214 

.70 

4.  61658 

.75 

4.  52367 

.25 

4.  57307 

.75 

4.  61743 

.80 

4.  52471 

.30 

4.  57401 

.80 

4.  61827 

.85 

4.  52576 

.35 

4.  57494 

.85 

4.  61911 

.90 

4.  52680 

.40 

4.  57587 

18 

.90 

4.  61995 

.95 

4.  52783 

.45 

4.  57679 

.95 

4.  62079 

21.00 

4.  52887 

.50 

4.  57772 

26.00 

4.  62162 

.05 

4.  52990 

.55 

4.  57864 

.05 

4.  62246 

.10 

4.  53093 

.60 

4.57956 

.10 

4.  62329 

.15 

4.  53196 

.65 

4.  58048 

.15 

4.  62412 

.20 

4.  53299 

20 

.70 

4.  58140 

.20 

4.  62495 

.25 

4.  53401 

.75 

4.  58231 

• 

.25 

4.  62578 

.30 

4.  53503 

.80 

4.58323 

.30 

4.  62661 

16 

.35 

4.  53605 

.85 

4.  58414 

.35 

4.  62743 

.40 

4.  53706 

.90 

4.  58505 

.40 

4.  62825 

.45 

4.53808 

.95 

4.  58596 

.45 

4.  62908 

304  GEOQRAPHTC    TABLES    AND    FORMULAS. 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

26.50 

4.  62990 

16 

29.00 

4.  66905 

15 

31.50 

4.  70496 

14 

.55 

4.  63071 

.05 

4.  66980 

.55 

4.  70565 

.60 

4.  63153 

* 

.10 

4.  67054 

.60 

4.  70634 

.65 

4.  63235 

.15 

4.67129 

.65 

4.  70702 

.70 

4.  63316 

.20 

4.  67203 

.70 

4.  70771 

.75 

4.  63397 

.25 

4.  67278 

.75 

4.  70839 

.80 

4.  63479 

.30 

4.  67352 

.80 

4.  70908 

.85 

4.  63559 

.35 

4.  67426 

.85 

4.  70976 

.90 

4.  63640 

.40 

4.  67500 

790 

4.  71044 

.95 

4.  63721 

• 

.45 

4.  67573 

.95 

4.71112 

27.00 

4.  63801 

.50 

4.  67647 

32.00 

4.71180 

.05 

4.  63882 

.55 

4.  67721 

.05 

4.  71248 

.10 

4.  63962 

.60 

4.  67794 

.10 

4.  71315 

.15 

4.  64042 

.65 

4.  67867 

.15 

4.  71383 

.20 

4.  64122 

.70 

4.  67941 

.20 

4.  71451 

13 

.25 

4.  64202 

.75 

4.  68014 

.25 

4.  71518 

.30 

4.  64281 

.80 

4.  68087 

.30 

4.  71585 

.35 

4.  64361 

.85 

4.68159 

.35 

4.  71652 

.40 

4.  64440 

.90 

4.  68232 

.40 

4.71719 

.45 

4.  64519 

.95 

4.  68305 

.45 

4.  71787 

.50 

4.  64598 

30.00 

4.  68377 

14 

.50 

4.  71853 

.55 

4.  64677 

.05 

4.  68449 

.55 

4.  71920 

.60 

4.  64756 

.10 

4..6S522 

.60 

4.  71987 

.65 

4.  64835 

.15 

4.  68594 

.65 

4.  72053 

.70 

4.  64913 

.20 

4.  68666 

.70 

4.  72120 

.75 

4.  64991 

.25 

4.  68737 

.75 

4.  72186 

.80 

4.  65069 

.30 

4.  68809 

.80 

4.  72252 

.85 

4.  65147 

.35 

4.  68881 

.85 

4.  72319 

.90 

4.  65225 

.40 

4.  68952 

.90 

4.  72385 

.95 

4.  65303 

.45 

4.  69024 

.95 

4.  72451 

28.00 

4.  65381 

15 

.50 

4.  69095 

33.00 

4.  72516 

.05 

4.  65458 

.55 

4.  69166 

.05 

4.  72582 

.10 

4.  65536 

.60 

4.  69237 

.10 

4.  72648 

.15 

4.  65613 

.65 

4.  69308 

.15 

4.  72713 

.20 

4.  65690 

.70 

4.  69379 

.20 

4.  72779 

.25 

4.  65767 

.75 

4.  69449 

.25 

4.  72844 

.30 

4.  65844 

.80 

4.  69520 

.30 

4.  72909 

.35 

4.  65920 

.85 

4.  69590 

.35 

4.  72975 

.40' 

4.  65997 

.90 

4.  69661 

.40 

4.  73040 

.45 

4.  66073 

.95 

4.  69731 

.45 

4.  73105 

.50 

4.  66149 

31.00 

4.  69801 

.50 

4.  73169 

.55 

4.  66226 

.05 

4.  69871 

.55 

4.  73234 

.60 

4.  66302 

.10 

4.  69941 

.60 

4.  73299 

.65 

4.  66377 

.15 

4.  70011 

.65 

4.  73363 

.70 

4.  66453 

.20 

4.  70081 

.70 

4.  73428 

.75 

4.  66529 

.25 

4.  70150 

.75 

4.  73492 

.80 

4.  66604 

.30 

4.  70219 

.80 

4.  73557 

.85 

4.  66680 

.35 

4.  70289 

.85 

4.  73621 

.90 

4.  66755 

.40 

4.  70358 

.90 

4.  73685 

.95 

4.  66830 

.45 

4.  70427 

.95 

4.73749 

GEOGRAPHIC    TABLES    AND    FORMULAS.  305 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log 
.01  mile 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

34.00 

4.  73813 

13 

36.  50 

4.  76894 

12 

39.00 

4.  79771 

11 

.05  |  4.73877 

.55 

4.  76954 

.05 

4.  79727 

.  10   4.  73940 

.60 

4.  77013 

.10 

4.  79883 

.  15   4.  74004 

.65 

4.  77072 

.15 

4.  79938 

.20   4.74068 

.70 

4.  77132 

.20 

4.  79994 

.25  .  4.74131 

.  75 

4.  77191 

.25 

4.80049 

.30   4.74194 

.80 

4.  77250 

.30 

4.  80104 

.35  i  4.74258 

.85 

4.  77309 

.35 

4.  80159 

.40   4.74321 

.90 

4.  77368 

.40 

4.  80215 

.45 

4.  74384 

.95 

4.  77426 

.45 

4.  80270 

.50 

4.74447 

37.00 

4.  77485 

.50 

4.80325 

.55 

4.  74510 

.05 

4.  77544 

.55 

4.  80380 

.60 

4.  74573 

.10 

4.  77602 

.60 

4.  80435 

.  .65 

4.  74635 

.15 

4.  77661 

.65 

4.  80489 

.70 

4.  74698 

.20 

4.  77719 

.70 

4.  80544 

.75 

4.  74761 

12 

.25 

4.  77778 

.75 

4.  80599 

.80 

4.  74823 

.30 

4.  77836 

.80 

4.  80653 

.85 

4.  74885 

.35 

4.  77894 

.85 

4.  80708 

.90 

4.  74947 

.40   4.77952 

.90 

4.  80762 

.  95   4.  75010 

.45   4.78010 

.95 

4.  80817 

35.  00   4.  75072 

.50  ;  4.78068 

40.00 

4.  80871 

.05  !  4.75134 

.55  1  4.78126 

.05 

4.  80925 

.  10   4.  75196 

.60 

4.  78184 

.10 

4.  80979 

.15 

4.  75257 

.65 

4.  78241 

.15 

4.  81034 

.20 

4.  75319 

.70 

4.  78299 

.20 

4.  81088 

.25 

4.  75381 

.75 

4.  78357 

.25   4.81142 

.30 

4.  75443 

.80 

4.  78414 

.30   4.81195 

.35 

4.  75504 

.85 

4.  78472 

.35  !  4.81249 

.40 

4.  75565 

.90 

4.  78529 

.40  i  4.81303 

.45 

4.  75627 

.95 

4.  78586 

.45  i  4.81357 

* 

.50 

4.  75688 

38.00 

4.  78643 

.50  ;  4.81411 

..55 

4.  75749 

.05 

4.  78701 

11 

.55   4.  81464 

.60 

4.  75810 

.10 

4.  78758 

.60 

4.  81518 

.65 

4.  75871 

.15 

4.  78815 

.65 

4.  81571 

.70 

4.  75932 

.20 

4.  78871 

.70 

4.  81624 

.75 

4.  75993 

.25 

4.  78928 

.75  I  4.81677 

.80 

4.  76053 

.30 

4.  78985 

.80 

4.81731 

.85 

4.  76114 

.35 

4.  79041 

.85 

4.  81784 

.90 

4.  76174 

.40 

4.  79098 

.90 

4.  81837 

.95 

4.  76235 

.45 

4.  79155 

.95 

4.  81890 

36.00 

4.  76295 

.50 

4.  79211 

41.00 

4.  81943 

.05 

4.  76355 

.55 

4.  79267 

.05 

4.  81996 

.10 

4.  76416 

.60 

4.  79324 

.10 

4.  82049 

.15 

4.  76476 

.65 

4.  79380 

.15 

4.82102 

.20 

4.  76536 

.70 

4.  79436 

.20 

4.  82155 

.25 

4.  76596 

.75 

4.  79592 

.25 

4.  82207 

.30 

4.  76656 

.80 

4.  79548 

.30 

4.  82260 

.35 

4.  76715 

.85 

4.  79604 

.35 

4.  82313 

10 

.40 

4.  76775 

.90 

4.  79660 

.40 

4.  82365 

.45 

4.  76835 

.95 

4.  79716 

.45 

4.  82417 

46001—08- 


•30 


306  GEOGRAPHIC  TABLES  AND  FORMULAS. 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log  j 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

41.50 

4.  82470 

10 

44.00 

4.  85010 

10 

46.50 

4.  87410 

9 

.55 

4.  82522 

.05 

4.  85060 

.55 

4.  87457 

.60 

4.  82574 

.10 

4.  85109 

.60 

4.  87504 

.65 

4.  82627 

.15 

4.  85158 

.65 

4.  87550 

.70 

4.  82679 

.20 

4.  85207 

.70 

4.  87597 

.75 

4.  82731 

.25 

4.  85256 

.75 

4.  87643 

.80 

4.  82783 

.30 

4.  85305 

.80 

4.  87690 

.85 

4.  82835 

.35 

4.  85354 

.85 

4.  87736 

.90 

4.  82886 

.40 

4.  85403 

.90 

4.  87782 

.95 

4.  82938 

.45 

4.  85452 

.95 

4.  87829 

42.00 

4.  82990 

.50 

4.  85501 

47.00 

4.  87875 

.05 

4.  83042 

.55 

4.  85550 

.05 

4.  87921 

.10 

4.  83093 

.60 

4.  85599 

.10 

4.  87967 

.15 

4.  83145 

.65 

4.  85647 

.15 

4.  88013 

.20 

4.83196 

.70 

4.  85696 

.20 

4.  88059 

.25 

4.  83248 

.75 

4.  85744 

.25 

4.  88105 

.30 

4.  83299 

.80 

4.  85793 

.30 

4.  88151 

.35 

4.  83350 

.85 

4.  85841 

.35 

4.  88197 

.40 

4:  83402 

.90 

4.  85890 

.40 

4.  88243 

.45 

4.  83453 

.95 

4.  85938 

.45 

4.  88289 

.50 

4.  83504 

45.00 

4.  85986 

.50 

4.  88334 

.55 

4.  83555 

.05 

4.  86035 

.55 

4.  88380 

.60 

4.  83606 

.10 

4.  86083 

.60 

4.  88326 

.65 

4.  83657 

.15 

4.  86131 

.65 

4.  88471 

.70 

4.  83708 

.20 

4.  86179 

.70 

4.  88517 

.75 

4.  83759 

.25 

4.  86227 

.75 

4.  88562 

.80 

4.  83809 

.30 

4.  86275 

.80 

4.  88608 

.85 

4.  83860 

.35 

4.  86323 

.85 

4.  88653 

.90 

4.  83911 

.40 

4.  86371 

.90 

4.  88699 

.95 

4.  83961 

.45 

4.  86418 

.95 

4.  88744 

43.00 

4.  84012 

.50 

4.  86466 

48.'  00 

4.  88789 

.05 

4.  84062 

.55 

4.86514 

.05 

4.  88834 

.10 

4.84113 

.60 

4.  86561 

.10 

4.  88879 

.15 

4.  84163 

.65 

4.  86609 

.15 

4.  88925 

.20 

4.  84213 

.70 

4.  86657 

.20 

4.  88970 

.25 

4.  84264 

.75 

4.  86704 

.25 

4.  89015 

.30 

4.  84314 

.80 

4.  86751 

.30 

4.  89060 

.35 

4.  84364 

.85 

4.  86799 

.35 

4.  89105 

.40 

4.  84414 

.90 

4.  86846 

.40 

4.  89149 

.45 

4.  84464 

.95 

4.  86894 

.45 

4.  89194 

.50 

4.  84514 

46.00 

4.  86941 

9 

.50 

4.  89239 

.55 

4.  84564 

.05 

4.  86988 

.55 

4.  89284 

.60 

4.  84614 

.10 

4.  87035 

.60 

4.  89329 

.65 

4.  84663 

.15 

4.  87082 

.65 

4.  89373 

.70 

4.  84713 

.20 

4.  87129 

.70 

4.  89418 

.75 

4.  84763 

.25 

4.  87176 

.75 

4.  89462 

.80 

4.  84812 

.30 

4.  87223 

.80 

4.  89507 

.85 

4.  84862 

.35 

4.  87270 

.85 

4.  89551 

.90 

4.  84911 

.40 

4.  87317 

.90 

4.  89596 

.95 

4.  84961 

.45 

4.  87364 

.95 

4.  89640 

GEOGRAPHIC    TABLES    AND    FORMULAS.  307 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.log. 
.01  mile. 

49.00 

4.  89685 

9 

51.50 

4.  91846 

8 

54.00 

4.  93904 

8 

.05 

4.  89729 

.55 

4.  91888 

.05 

4.  93945 

.10 

4.  89773 

.60 

4.  91930 

.10 

4.  93985 

.15 

4.  89817 

.65 

4.  91972 

.15 

4.  94025 

.20 

4.  89861 

.70 

4.  92014 

.20 

4.  94065 

.25 

4.  89906 

.75 

4.  92056 

.25 

4.  94105 

.30 

4.  89950 

.80 

4.  92098 

.30 

4.  94145 

.35 

4.89994 

.85 

4.  92140 

.35 

4.  94185 

.40 

4.  90038 

.90 

4.  92182 

.40 

4.  94225 

.45 

4.  90082 

.95 

4.  92224 

.45 

4.  94265 

.50 

4.  90125 

52.00 

4.  92265 

.50 

4.  94305 

.55 

4.  90169 

.05 

4.  92307 

.55 

4.  94345 

.60 

4.  90213 

.10 

4.  92349 

.60 

4.  94384 

.65 

4.  90257 

.15 

4.  92390 

.65 

4.94424 

.70 

4.  90301 

.20 

4.  92432 

.70 

4.  94464 

.75 

4.  90344 

.25 

4.  92474 

.75 

4.  94503 

.80 

4.  90388 

.30 

4.  92515 

.80 

4.  94543 

.85 

4.  90431 

.35 

4.  92557 

.85 

4.  94583 

.90 

4.  90475 

.40 

4.  92598 

.90 

4.  94622 

.95 

4.  90519 

.45 

4.  92639 

.95 

4.  94662 

50.00 

4.  90562 

.50 

4.  92681 

55.  00 

4.  94701 

.05 

4.  90605 

.55 

4.  92722 

.05 

4.  94741 

.10 

4.90649 

.60 

4.  92764 

.10 

4.  94780 

.15 

4.90692 

.65 

4.  92805 

.15 

4.  94820 

.20 

4.  90735 

.70 

4.  92846 

.20 

4.  94859 

.  25   4.  90779 

.75 

4.  92887 

.25 

4.  94898 

.30 

4.  90822 

.80 

4.  92928 

.30 

4.  94937 

.35 

4.  90865 

.85 

4.  92969 

.35 

4.  94977 

.40 

4.  90908 

.90 

4.  93011 

.40 

4.  95016 

.45 

4.90951 

.95 

4.  93052 

.45 

4.  95055 

.50 

4.90994 

53.00 

4.  93093 

.50 

4.  95094 

.55 

4.  91037 

.05 

4.  93133 

.55 

4.  95133 

.60 

4.  91080 

.10 

4.  93175 

.60 

4.  95172 

.65 

4.  91123 

.15 

4.  93215 

.65 

4.  95212 

.70 

4.  91166 

.20 

4.  93256 

.70 

4.  95251 

.75 

4.  91209 

.25 

4.  93297 

V 

.75 

4.  95289 

.80 

4.  91251 

.30 

4.  93338 

.80 

4.  95328 

.85 

4.  91294 

.35 

4.  93378 

.85 

4.  95367 

.90 

4.  91337 

.40 

4.  93419 

.90 

4.  95406 

.95 

4.  91379 

.45 

4.  93460 

.95 

4.  95445 

51.00 

4.  91422 

.50 

4.  93500 

56.00 

4.  95484 

.05 

4.  91465 

.55 

4.  93541 

.05 

4.  95523 

.10 

4.  91507 

.60 

4.  93581 

.10 

4.  95561 

.15 

4.  91550 

.65 

4.  93622 

.15 

4.  95600 

.20 

4.  91592 

.70 

4.  93662 

.20 

4.  95639 

.25 

4.  91634 

.75 

4.  93703 

.25 

4.  95677 

.30 

4.  91677 

8 

.80 

4.  93743 

.30 

4.  95716 

.35 

4.91719 

.85 

4.  93784 

.35 

4.  95754 

.40 

4.  91761 

.90 

4.  93824 

.40 

4.  95793 

.45 

4.  91803 

.95 

4.  93864 

.45 

4.  95831 

308  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  31. — For  interconverslon  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

56.50 

4.  95870 

8 

59.00 

4.  97750 

7 

61.50 

4.  99553 

7 

.55 

4.  95908 

.05 

4.  97787 

.55 

4.  99588 

.60 

4.  95947 

.10 

4.  97824 

.60 

4.  99623 

.65 

4.  95985 

.15 

4.  97861 

.65 

4.  99658 

.70 

4.96023 

:20 

4.  97897 

.70 

4.  99693 

.75 

4.  96062 

.25 

4.  97934 

.75 

4.  99729 

.80 

4.  96100 

.30 

4.  97971 

.80 

4.  99764 

.85 

4.  96138 

.35 

4.  98007 

.85 

4.  99799 

.90 

4.  96176 

.-40 

4.  98044 

.90 

4.  99834 

.95 

4.  96214 

.45 

4.  98080 

.95 

4.  99869 

57.00 

4.  96253 

.50 

4.  98117 

62.00 

4.  99904 

.05 

4.  96291 

'  .55 

4.  98153 

.05 

4.  99939 

.10 

4.  96329 

.60 

4.  98190 

.10 

4.  99974 

.15 

4.  96367" 

.65 

4.  98226 

.15 

5.  00009 

.20 

4.  96405 

.70 

4.  98262 

.20 

5.  00044 

.25 

4.  96443 

.75 

4.  98299 

.25 

5.  00079 

.30 

4.  96481 

.80 

4.  98335 

.30 

5.  00114 

.35 

4.96518 

.85 

4.  98371 

.35 

5.00149 

.40 

4.  96556 

.90 

4.  98408 

.40 

5.  00183 

.45 

4.  96594 

.95- 

4.  98444 

.45 

5.  00218 

.50 

4.  96632 

V60.  00 

4.  98480 

.50 

5.  00253 

.55 

4.  96669 

.05 

4.  98516 

.55 

5.  00288 

.60 

4.  96707 

.10 

4.  98552 

.60 

5.  00322 

.65 

4.  96745 

.15 

4.  98589 

.65 

5.  00357 

.70 

4.  96783 

.20 

4.  98625 

.70 

5.  00392 

.75 

4.  96820 

.25 

4.  98661 

.75 

5.00426 

.80 

4.  96858 

7  . 

.30 

4.  98697 

.80 

5.  00461 

.85 

4.  96895 

.35 

4.  98733 

.85 

5.  00495 

.90 

4.  96933 

.40 

4.  98769 

.90 

5.  00530 

.95 

4.  96970 

.45 

4.  98805 

.95 

5.  00565 

58.00 

4.  97008 

.50 

4.  98841 

63.00 

5.  00599 

.05 

4.  97045 

.55 

4.  98876 

.05 

5.  00633 

.10 

4.  97083 

.60 

4.  98912 

.10 

5.  00668 

.15 

4.  97120 

.65 

4.  98948 

.15 

5.  00702 

.20 

4.  97157 

.70 

4.  98984 

.20 

5.  00737 

.25 

4.  97195 

-.75 

4.  99020 

.25 

5.  00771 

.30 

4.  97232 

.80 

4.  99055 

.30 

5.  00805 

.35 

4.97269 

.85 

4.  99091 

.35 

5.  00840 

.40 

4.  97306 

.90 

4.  99127 

.40 

5.  00874 

.45 

4.97343 

.95 

4.  99162 

.45 

5.  00908 

I 

.50 

4.  97381 

61.00 

4.  99198 

.50 

5.  00942 

.55 

4.  97418 

.05 

4.  99234 

.55 

5.  00977 

.60 

4.  97455 

.10 

4.  99269 

.60 

5.01011 

.65 

4.  97492 

.15 

4.  99305 

.65 

5.01045 

.70 

4.  97529 

.20 

4.  99340 

.70 

5.  01079 

.75 

4.  97566 

.25 

4.  99376 

.75 

5.  01113 

.80 

4.97603 

.30 

4.  99411 

.80 

5.  01147 

.85 

4.  97640 

.35 

4.  99447 

.85 

5.01181 

.90 

4.  97677 

.40 

4.  99482 

.90 

5.  01215 

.95 

4.  97713 

.45 

4.  99517 

.95 

5.  01249 

GEOGRAPHIC   TABLES    AND   FORMULAS.  309 

TABLE  31. — For  inter  conversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.log. 
.01  mile. 

Miles.  Log.  meters. 

| 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.log. 
.01  mile. 

64.00 

5.  01283 

7 

66.50 

5.  02947 

7 

69.  00 

5.  04550 

6 

.05 

5.  01317 

.55 

5.  02980 

.05 

5.  04581 

.10 

5.  01351 

.60 

5.  03012 

.10 

5.  04613 

.15 

5.  01385 

.65 

5.  03045 

.15 

5.  04644 

.20 

5.  01419 

.70 

5.  03078 

.20 

5.  04676 

.25 

5.  01452 

.75 

5.  03110 

.25 

5.  04707 

.30 

5.  01486 

.80 

5.03143 

.30 

5.  04738 

.35 

5.  01520 

.85 

5.03175 

.35 

5.  04770 

.40 

5.  01554 

.90 

5.  03208 

.40 

5.  04801 

.45 

5.  01587 

.95 

5.  03241 

.45 

5.  04832 

.50 

5.  01621 

67.00 

5.  03273 

6 

.50 

5.  04863 

.55 

5.  01655 

.05 

5.  03305 

.55 

5.  04895 

.60 

5.  01688 

.10 

5.  03337 

.60 

5.  04926 

.65 

5.  01722 

.15 

5.  03370 

.65 

5.  04957 

.70 

5.  01755 

.20 

5.  03402 

.70 

5.  04988 

.75 

5.  01789 

.25 

5.  03434 

.75 

5.05019 

.80 

5.  01823 

.30 

5.  03467 

.80 

5.  05051 

.85 

5.  01856 

.35 

5.  03499 

.85 

5.  05082 

.90 

5.  01889 

.40 

5.  03531 

.90 

5.  05113 

.95 

5.  01923 

.45 

5.  03563 

.95 

5.  05144 

65.00 

5.  01956 

.50 

5.  03595 

70.00 

5.  05175 

.05 

5.  01990 

.55 

5.  03627 

.05 

5.  05206 

.10 

5.  02023 

.60 

5.  03660 

.10 

5.  05237 

.15 

5.  02056 

.65 

5.  03692 

.15 

5.  05268 

.20 

5.02090 

.70 

5!  03724 

.20 

5.  05299 

.25 

5.  02123 

.75 

5.  03756 

.25 

5.  05330 

.30 

5.  02156 

.80 

5.  03788 

.30 

5.  05361 

.35 

5.  02190 

.85 

5.  03820 

.35 

5.  05391 

.40 

5.  02223 

.90 

5.  03852 

.40 

5.  05422 

.45 

5.  02256 

.95 

5.  03884 

.45 

5.  05453 

.50 

5.  02289 

68.00 

5.  03916 

.50 

5.  05484 

.55 

5.  02322 

.05 

5.  03948 

.55 

5.  05515 

.60 

5.  02355 

.10 

5.  03980 

.60 

5.  05545 

.65 

5.  02389 

.15 

5.  04012 

.65 

5.  05576 

.70 

5.  02421 

.20 

5.  04043 

.70 

5.  05607 

.75 

5.  02455 

.25 

5.  04075 

.75 

5.  05538 

.80 

5.  02488 

.30 

5.  04107 

.80 

5.  05668 

.85 

5.  02521 

.35 

5.  04139 

.85 

5.  05699 

.90 

5.  02554 

.40 

5.  04171 

.90 

5.  05730 

.95 

5.  02587 

.45 

5.  04202 

.95 

5.  05760 

66.00 

5.  02619 

.50 

5.  04234 

71.00 

5.  05791 

.05 

5.  02652 

.55 

5.  04266 

.05 

5.05821 

.10 

5.  02685 

.60 

5.  04297 

.10 

5.  05852 

.15 

5.  02718 

.65 

5.  04329 

.15 

5.  05883 

.20 

5.  02751 

.70 

5.  04361 

.20 

5.  05913 

.25 

5.  02784 

.75 

5.  04392 

.25 

5.  05943 

.30 

5.  02816 

.80 

5.  04424 

.30 

5.  05974 

.35 

5.  02849 

.85 

5.  04455 

.35 

5.06004 

.40 

5.  02882 

.90 

5.  04487 

.40 

5.  06035 

.45 

5.  02915 

.95 

5.  04518 

.45 

5.06065 

310  GEOGRAPHIC   TABLES    AND   FORMULAS. 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

71.50 

5.  06096 

6 

74.00 

5.  07588 

6 

76.50 

5.  09031 

6 

.55 

5.  06126 

.05 

5.  07617 

.55 

5.  09059 

.60 

5.  06156 

.10 

5.  07647 

.60 

5.  09088 

.65 

5.  06187 

.15 

5.  07676 

.65 

5.  09117 

.70 

5.  06217 

.20 

5.  07705 

.70 

5.  09145 

.75 

5.  06247 

.25 

5.  07735 

.75 

5.  09173 

.80 

5.  06277 

.30 

5.  07764 

.80 

5.  09201 

.85 

5.  06308 

.35 

5.  07793 

.85 

5.  09229 

.90 

5.  06338 

.40 

5.  07822 

.90 

5.  09258 

.95 

5.  06368 

.45 

5.  07851 

.95 

5.  09286 

72.00 

5.  06398 

.50 

5.  07881 

77.00 

5.  09314 

.05 

5.  06428 

.55 

5.  07910 

.05 

5.  09342 

.10 

5.06459 

.60 

5.  07939 

.10 

5.  09370 

.15 

5.  06489 

.65 

5.  07968 

.15 

5.  09399 

.20 

5.  06519 

.70 

5.  07997 

.20 

5.  09427 

.25 

5.  06549 

.75 

5.  08026 

.25 

5.  09455 

.30 

5.  06579 

.80 

5.  08055 

.30 

5.  09483 

.35 

5.  06609 

.85 

5.  08084 

.35 

5.  09511 

.40 

5.  06639 

.90 

5.08113 

.40 

5.  09539 

.45 

5.  06669 

.95 

5.  08142 

.45 

5.  09567 

.50 

5.  06699 

75.00 

5.  08171 

.50 

5.  09595 

.55 

5.  06729 

.05 

5.  08200 

.55 

5.  09623 

.60 

5.  06759 

.10 

5.  08229 

.60 

5.  09651 

.65 

5.  06789 

.15 

5.  08258 

.65 

5.  09679 

.70 

5.  06818 

.20 

5.  08287 

.70 

5.  09707 

.75 

5.06848 

.25 

5.  08316 

.75 

5.  09735 

.80 

5.  06878 

.30 

5.  08345 

.80 

5.  09763 

.85 

5.  06908 

.35 

5.  08373 

.85 

5.  09791 

.90 

5.  06938 

.40 

5.  08402 

.90 

5.  09819 

.95 

5.  06967 

.45 

5.  08431 

.95 

5.  09847 

73.00 

5.  06997 

.50 

5.  08460 

78.00 

5.  09875 

.05 

5.  07027 

.55 

5.  08488 

.05 

5.  09902 

.10 

5.  07057 

'  .60 

5.  08517 

.10 

5.  09930 

.15 

5.  07086 

.65 

5.  08546 

.15 

5.  09958 

.20 

5.07116 

.70 

5.  08575 

.20 

5.  09986 

.25 

5.  07146 

.75 

5.  08603 

.25 

5.  10013 

.30 

5.  07175 

.80 

5.  08632 

.30 

5.  10041 

.35 

5,07205 

.85 

5.  08661 

.35 

5.  10069 

.40 

5.  07235 

.90 

5.  08689 

.40 

5.  10097 

.45 

5.  07264 

.95 

5.  08718 

.45 

5.  10124 

.50 

5.  07294 

76.00 

5.  08746 

.50 

5.10152 

.55 

5.  07323 

.05 

5.  08775 

.55 

5.  10180 

.60 

5.  07353 

.10 

5.  08803 

.60 

5.  10207 

.65 

5.  07382 

.15 

5.  08832 

.65 

5.  10235 

.70 

5.  07412 

.20 

5.  08861 

.70 

5.  10263 

.75 

5.  07441 

.25 

5.  08889 

.75 

5.  10290 

.80 

5.  07471 

.30 

5.  08917 

.80 

5.  10318 

.85 

5.  07500 

.35 

5.  08946 

.85 

5.  10345 

.90 

5.  07529 

.40 

5.  08974 

.90 

5.  10373 

.95 

5.07559 

.45 

5.  09003 

.95 

5.  10400 

GEOGRAPHIC    TABLES    AtfD    FORMULAS.  311 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
01  mile. 

79.00 

5.10428 

5 

81.50 

5.  11781 

5 

84.00 

5.  13093 

'  5 

.05 

5.  10455 

.55 

5.  11807 

.05 

5.  13119 

.10 

5.  10483 

.60 

5.  11834 

.10 

5.  13145 

.15 

5.  10510 

.65 

5.  11861 

.15 

5.13170. 

.20 

5.  10537 

.70 

5.  11887 

.20 

5.  13196 

.25 

5.  10565 

.75 

5.11913 

.25 

5.  13222 

.30 

5.  10592 

.80 

5.  11940 

.30 

5.  13248 

.35 

5.  10620 

.85 

5.  11967 

.35 

5.  13273 

.40 

5.  10647 

.90 

5.  11993 

.40 

5.  13299 

.45 

5.  10674 

.95 

5.  12020 

.45 

5.  13325 

.50 

5.  10702 

82.00 

5.  12046 

.50 

5.  13351 

.55 

5.  10729 

.05 

5.  12073 

.55 

5.  13376 

.60 

5.  10756 

.10 

5.12099 

.60 

5.  13402 

.65 

5.  10784 

.15 

5.12126 

.65 

5.  13428 

.70 

5.  10811 

.20 

5.  12152 

.70 

5.  13453 

.75 

5.  10838 

.25 

5.  12179 

.75 

5.  13479 

.80 

5.  10865 

.30 

5.  12205 

.80 

5.13505 

.85 

5.  10893 

.35 

5.12231 

.85 

5.  13530 

.90 

5.  10920 

.40 

5.  12258 

.90 

5.  13556 

/ 

.95 

5.  10947 

.45 

5.  12284 

.95 

5.  13581 

80.00 

5.  10974 

.50 

5.  12310 

85.00 

5.  13607 

.05 

5.11001 

.55 

5.12337 

.05 

5.  13632 

.10 

5.11028 

.60 

5.  12363 

.10 

5.  13658 

.15 

5.  11055 

.65 

5.  12389 

.15 

5.  13683 

.20 

5.  11082 

.70 

5.  12416 

.20 

5.  13709 

.25 

5.11109 

.75 

5.  12442 

.25 

5.  13734 

.30 

5.11137 

.80 

5.  12468 

.30 

5.  13760 

.35 

5.11164 

.85 

5.  12494 

.35 

5.  13785 

.40 

5.  11191 

.90 

5.  12521 

.40 

5.  13811 

.45 

5.11218 

.95 

5.  12547 

.45 

5.  13836 

.50 

5.  11245 

83.00 

5.  12573 

.50 

5.  13862 

.55 

5.  11272 

.05 

5.  12599 

.55 

5.  13887 

.60 

5.  11299 

.10 

5.12625 

.60 

5.  13912 

.65 

5.  11325 

.15 

5.  12651 

.65 

5.  13938 

.70 

5.11352 

.20 

5.  12677 

.70 

5.  13963 

.75 

5.  11379 

.25 

5.  12703 

.75 

5.  13988 

.80 

5.  11406 

.30 

5.  12729 

.80 

5.  14014 

.85 

5.  11433 

.35 

5.  12756 

.85 

5.  14039 

.90 

5.  11460 

.40 

5.  12782 

.90 

5.  14064 

.95 

5.  11487 

.45 

5.  12808 

.95 

5.  14090 

81.00 

5.  11513 

.50 

5.  12834 

86.00 

5.  14115 

.05 

5.  11540 

.55 

5.  12860 

.05 

5.  14140 

.10 

5.  11567 

.60 

5.  12886 

.10 

5.  14165 

.15 

5.  11594 

.65 

5.  12912 

.15 

5.  14191 

.20 

5.  11621 

.70 

5.  12937 

.20 

5.  14216 

.25 

5.  11647 

.75 

5.  12963 

.25 

5.  14241 

.30 

5.  11674 

.80 

5.  12989 

.30 

5.  14266 

.35 

5.  11701 

.85 

5.  13015 

.35 

5.  14291 

.40 

5.11727 

.90 

5.  13041 

.40 

5.  14316 

.45 

5.  11754 

.95 

5.  13067 

.45 

5.  14341 

312  GEOGRAPHIC    TABLES    AND    FORMULAS. 

TABLE  31. — For  interconversion.  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

86.50 

5.  14367 

5 

89.00 

5.  15604 

5 

91.50 

5.  16807 

5 

.55 

5.  14392 

.05 

5.  15628 

.55 

5.  16831 

.60 

5.  14417 

.10 

5.  15653 

.60 

5.  16855 

.65 

5.  14442 

.15 

5.  15677 

.65 

5.  16878 

.70 

5.  14467 

.20 

5.  15701 

.70 

5.  16902 

.75 

5.  14492 

.25 

5.  15726 

.75 

5.  16926 

.80 

5.  14517 

.30 

5.  15750 

.80 

5.  16949 

.85. 

5.  14542 

.35 

5.  15775 

.85 

5.  16973 

.90 

5.  14567 

.40 

5.  15799 

.90 

5.  16997 

.95 

5.  14592 

.45 

,  5.15823 

.95 

5.  17020 

87.00 

5.  14617 

.50 

5.  15847 

92.00 

5.  17044 

.05 

5.  14642 

.55 

5.  15872 

.05 

5.17067 

.10 

5.  14667 

.60 

5.  15896 

.10 

5.  17091 

.15 

5.  14692 

.65 

5.  15920 

.15 

5.17115 

.20 

5.  14717 

.70 

5.  15944 

.20 

5.  17138 

.25 

5.  14741 

.75 

5.  15968 

.25 

5.  17162 

.30 

5.  14766 

.80 

5.  15993 

.30 

5.17285 

.35 

5.  14791 

.85 

5.  16017 

.35 

5.  17209 

.40 

5.  14816 

.90 

5.  16041 

.40 

5.  17232 

.45 

5.  14841 

.95 

5.  16065 

.45 

5.  17256 

.50 

5.  14866 

90.00 

5.  16089 

.50 

5.  17279 

.55 

5.  14891 

.05 

5.  16113 

.55 

5.  17303. 

.60 

5.  14915 

.10 

5.  16137 

.60 

5.  17326 

.65 

5.  14940 

.15 

5.  16162 

.65 

5.  17349 

.70 

5.  14965 

.20 

5.  16186 

.70 

5.17373 

.75 

5.  14990 

.25 

5.  16210 

.75 

5.  17396 

.80 

5.  15014 

.30 

5.  16234 

.80 

5.17420 

.85 

5.  15039 

.35 

5.  16258 

.85 

5.17443 

.90 

5.  15064 

.40 

5.  16282 

.90 

5.17467 

.95 

5.  15089 

.45 

5.  16306 

.95 

5.17490 

88.00 

5.  15113 

.50 

5.  16330 

93.00 

5.  17513 

.05 

5.  15138 

.55 

5.  16354 

.05 

5.  17537 

.10 

5.  15163 

.60 

5.  16378 

.10 

5.17560 

.15 

5.  15187 

.65 

5.  16402 

.15 

5.  17583 

.20 

5.  15212 

.70 

5.  16426 

.20 

5.  17607 

.25 

5.  15237 

.75 

5.  16450 

.25 

5.  17630 

.30 

5.  15261 

.80 

5.  16474 

.30 

5.17653 

,  . 

.35 

5.  15286 

.85 

5.  16497 

.35 

5.17676 

.40 

5.  15310 

.90 

5.  16521 

.40 

5.  17700 

.45 

5:  15335 

.95 

5.  16545 

.45 

5.  17723 

.50 

5.  15359 

91.00 

5.  16569 

.50 

5.  17746 

.55 

5.  15384 

.05 

5.  16593 

.55 

5.  17769 

.60 

5.  15408 

.10 

5.  16617 

.60 

5.  17793 

.65 

5.  15433 

.15 

5.  16641 

.65 

5.  17816 

.70 

5.  15457 

.20 

5.  16665 

.70 

5.  17839 

.75 

5.  15482 

.25 

5.  16688 

.75 

5.  17862 

.80 

5.  15506 

.30 

5.  16712 

.80 

5.17885 

.85 

5.  15531 

.35 

5.16736 

.85 

5.  17908 

.90 

5.  15555 

.40 

5.  16760 

.90 

5.  17932 

.95 

5.  15580 

.45 

5.  16783 

.95 

5.  17955 

GEOGRAPHIC    TABLES    AND    FORMULAS.  313 

TABLE  31. — For  interconversion  of  miles  and  logarithms  of  meters — Continued. 


Miles. 

Log.  meters. 

Diff.log 
.01  mile 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

Miles. 

Log.  meters. 

Diff.  log. 
.01  mile. 

94.00 

5.  17978 

5 

96.00 

5.  18892 

5 

98."  00 

5.  19788 

4 

.05 

5.  18001 

• 

.05 

5.  18915 

.05 

5.  19810 

.10 

5.  18024 

.10 

5.  18937 

.10 

5.  19832 

.15  !  5.18047 

.15 

5.  18960 

.15 

5.19854 

.20 

5.  18170 

.20 

5.  18983 

.20 

5.  19876 

.25 

5.  18193 

.25 

5.  19005 

.25 

5.  19898 

.30 

5.  18116 

.30 

5.  19028 

.30 

5.  19920 

.35 

5.  18139 

.35 

5.  19050 

.35 

5.  19942 

.40 

5.  18162 

.40 

5.  19073 

.40 

5.  19965 

.45 

5.  18185 

.45 

5.  19095 

.45 

5.  19987 

.50 

'  5.18208 

.50 

5.  19118 

.50 

5.  20009 

.55 

5.  18231 

.55 

5.  19140 

.55 

5.  20031 

.60 

5.  18254 

.60 

5.  19163 

.60 

5.  20053 

.65 

5.  18277 

.65 

5.  19185 

.65 

5.  20075 

.70 

5.  18300 

.70 

5.  19208 

.70 

5.  20097 

.  75   5.  18323 

.75 

5.  19230 

.75 

5.  20119 

.  80   5.  18346 

.80 

5.  19253 

.80 

5.  20141 

.  85   5.  18369 

.85 

5.  19275 

.85 

5.  20163 

.90 

5.  18392 

.90 

5.  19297 

.90 

5.  20185 

.95 

5.  18415 

.95 

5.  19320 

.95 

5.  20207 

95.00 

5.  18437 

97.00 

5.  19342 

4 

99.00 

5.  20229 

.05 

5.  18460 

.05 

5.  19365 

.05 

5.  20250 

.10 

5.  18483 

.10 

5.  19387 

.10 

5.  20272 

.15 

5.18506 

.15 

5.  19409 

.15 

5.  20294 

.20 

5.  18529 

.20 

5.  19432 

.20 

5.  20316 

.25 

5.  18551 

.25 

5.  19454 

.25 

5.  20338 

.30 

5.18574 

.30 

5.  19476 

.30 

5.  20360 

.  .35 

5.  18597 

.35 

5.  19499 

.,35 

5.  20382 

.40 

5.  18620 

.40 

5.  19521 

.40 

5.  20404 

.45 

5.  18643 

.45 

5.  19543 

.45 

5.  20425 

.50 

5.18665 

.50 

5.  19565 

.50 

5.  20447 

.55 

5.  18688 

.55 

5.  19588 

.55 

5.  20469 

.60 

5.  18711 

.60 

5.  19610 

.60 

5.  20491 

.65 

5.  18733 

.65 

5.  19632 

.65 

5.  20513 

.70 

5.  18756 

.70 

5.  19655 

.70 

5.  20535 

.75 

5.  18779 

.75 

5.  19677 

.75 

5.  20556 

.80 

5.  18802 

.80 

5.  19699 

.80 

5.  20578 

.85 

5.  18824 

.85 

5.  19721 

.85 

5.  20600 

.90 

5.  18847 

.90 

5.  19743 

.90 

5.  20621 

.95 

5.  18869 

.95 

5.  19765 

.95 

5.  20643 

1  acre  =209  feet  square,  nearly. 

1  acre  =  43,560  square  feet  =  4,840  square  yards. 

1  statute  mile  =  1,760  yards  =  5,280  feet  =  63,360  inches. 

1  cubic  foot  =  7.48  gallons  =  0.804  bushel. 

1  cubic  foot  of  water  weighs  62.4  pounds. 

1  wine  gallon  =  8.34  pounds  water. 

1  wine  gallon  =  231  cubic  inches. 

1  avoirdupois  pound  =  7,000  grains. 

1  troy  pound  =  5,760  grains. 


314          GEOGRAPHIC  TABLES  AND  FORMULAS. 

1  meter  =?  39.37  inches.     Log.  1.5951654. 

1  meter  =  3.28083  feet.     Log.  0.5159842. 

1  meter  =  1.093611  yards.     Log.  0.0388629. 

1  meter  =  0.00062137  mile.     Log.  6.7933502. 

1  kilometer  =  3,281  feet  =  five-eighths  mile,  nearly. 

1  cubic  meter  =  35.314  cubic  feet  =  1.308  yards. 

1  liter  =  1.0567  quarts. 

1  gram  =  15.43  grains. 

1  kilogram  =  2.2046  avoirdupois  pounds. 

1  tonneau  (metric  ton)  =  2,204.6  pounds. 

1  cubic  meter  per  minute  =  0.5886  second-foot. 

1  second-foot  =  50  California  miner's  inches. 

1  second-foot  =  40  Arizona  miner's  inches. 

1  second-foot  =  449  gallons  per  minute. 

1  second-foot  for  one  day  =  1.9835  acre-feet. 

1  second-foot  for  one  day  =  646,272  United  States  gallons. 

1  second-foot  =  about  one  acre-inch  per  hour. 

1  acre-foot  =  325,850  gallons. 

1,000,000  gallons  =  3.07  acre-feet. 

1,000,000  cubic  feet  =  22.95  acre-feet. 

1,000,000  gallons  per  24  hours  =  1.55  second-feet. 

1  horse  power  =  550  foot-pounds  per  second. 

1  horse  power  =  76  kilogrammeters  per  second. 

1  horse  power  =  746  watts. 

1  horse  power  =  1  second-foot  water  falling  8.8  feet. 

1  second-foot  falling  10  feet  —  1.135  horse  power. 

1  foot  per  second  =  1.077  kilometers  per  hour. 

1  foot  per  second  =  0.68  miles  per  hour. 

1  inch  =  2.54  centimeters. 

1  foot  =  0.3048  meters. 

1  yard  =  0.9144  meters. 

1  mile  =  1.60935  kilometers. 

1  square  yard  =  0.836  square  meters. 

1  acre  =  0.4047  hectares. 

1  square  mile  =  259  hectares. 

1  square  mile  =  2.59  square  kilometers. 

1  cubic  foot  =  0.0283  cubic  meters. 

1  cubic  yard  =  0.7646  cubic  meters. 

1  gallon  =  3. 7854  liters. 

1  pound  =  0.4536  kilograms. 

{15  pounds  per  square  inch. 
1  ton  per  square  foot. 
1  kilo  per  square  centimeter. 
Acceleration  of  gravity  =  32.16  feet  per  second. 
To  change  miles  to  inches  on  map: 

Scale  1: 125000,  1  mile  =  0.50688  inches.     Log.  =  9.7049052. 
Scale  1 : 90000,    1  mile  =  0. 70400  inches.     Log.  =  9. 8475727. 
Scale  1:62500,    I  mile  =  1.01376  inches.     Log.  =  0.0059352. 
Scale  1:45000,    1  mile  =  1.40800  inches.     Log.  =  0.1486027. 
To  change  log.  of  meters  to  log.  of  inches  on  map : 
Scale  1:125000  add  6.4982552. 
Scale  1:90000    add  6.6409228. 
Scale  1 : 62500    add  6. 7992853. 
Scale  1:45000    add  6.9419528. 


GEOGRAPHIC    TABLES    AND    FORMULAS. 


315 


CONSTANTS. 


Basis  of  natural  logarithms       .  ... 

e  = 

2.  7182818285 
0.  4342944819 
206264.  8062 
3437.  74677 
57.  2957795 
1296000 
21600 
360 
1 
3.  1415926536 

Log. 
0.  4342944819 
9.  6377843113-10 
5.  3144251332 
3.  5362738828 
1.  7581226324 
6.  1126050015 
4.  3344537512 
2.  5563025008 
0.  0000000000 
0.4971498727 

Modulus  of  Briggs's  logarithms 

Radius  of  the  circle  in  seconds 

r  — 

Radius  of  the  circle  in  minutes 

r  — 

Radius  of  the  circle  in  degrees            . 

r  = 

Circumference  of  the  circle  in  seconds 

Circumference  of  the  circle  in  minutes 

Circumference  of  the  circle  in  degrees  

Circumference  of  the  circle  for  the  diameter.  = 

ASTRONOMICAL   CONSTANTS    (HABKNESS). 

Sidereal  year  =  365.256  357  8  mean  solar  days. 
Sidereal  day  =  23h  56m  4.S100  mean  solar  time. 
Mean  solar  day  =  24h  3m  56.9546  sidereal  time. 
Mean  distance  of  the  earth  from  the  sun  =  92  800  000  miles. 

PHYSICAL   CONSTANTS. 

Velocity  of  light  (Harkness)  =  186  337  miles  per  second  =  299  878  km.  per  second. 
Velocity  of  sound  through  dry  air  =  1090  v/1 +0.00367  t°  C.  feet  per  second. 


LINEAR  EXPANSIONS  OF  PRINCIPAL.  METALS  IN  MICRONS 
PER  METER  (OR  MILLIONTHS  PER  UNIT  LENGTH). 


Name  of  metal. 

Expansion 
per 
degree  C. 

Expansion 
per 
degree  F. 

Aluminum 

20 

11.1 

Brass                                                                      

19 

10.5 

Copper  .  . 

17 

9.4 

Glass                      

9 

5.0 

Gold 

15 

8.3 

Iron   cast 

11 

6.1 

Iron,  wrought.   .   

12 

6.7 

Lead 

28 

15.5 

Nickel-steel           ...  

0 

0.0 

Platinum           

9 

5  0 

Platinum-iridium 

8  7 

4  8 

Silver  ,  

19 

10.5 

Steel,  hard 

12 

6  7 

Steel,  soft  

11 

6  1 

Tin 

19 

10  5 

Zinc  

29 

16  1 

INDEX. 


Page. 

Alidades,  micrometer,  determination  of  con- 
stant and  value  of  division 12-13 

Altitude,  differences  of,  table  for  obtain- 
ing   274-289 

Arc  into  time,  table  for  conversion  of Ill 

Astronomical  constants 315 

Azimuths  of  Polaris  at  any  hour  angle,  ex- 
planation of 22-25 

at  any  hour  angle,  table  of 20-21 

at  elongation,  table  of 19 

Center,  reduction  to,  example  cf 7 

reduction  to,  figure  and  formula  for 6 

reduction  to,  graphic 8 

Circular   functions   expressed   in   arc   and 
time,  five-place  logarithm  table 

of 148-192 

Constants,  table  of 315 

Culminations  of  Polaris,  table  giving  times 

of 16 

examples  for  computing  times  of 18 

Curvature  and  refraction,  table  of  correc- 
tions for 273 

Elongations  of  Polaris,  table  of  azimuth  at.        19 

table  of  times  of 16 

Equivalents,  convenient,  table  of 313-314 

Expansion,  linear,  of  metals 315 

Feet  to  decimals  of  a  mile,  table  for  conver- 
sion of 115 

Feet  to  meters,  table  for  conversion  of 268 

Geodetic  position  computations,  formulas 

and  constants  for 193 

inverse  solution,  example  of. 270 

logarithms  of  factors  A,  B,  C,  D,  E,  F, 

latitude  0°-72° 193-270 

Hour  angle  of  Polaris 14 

Kilometers  to  statute  miles,  table  for  con- 
version of 268 

Logarithms  of  circular  functions  expressed 
in  arc  and  time,  five-place  table 

of 148-192 

of   natural    numbers,    five-place   table 

of 126-147 

Longitude  corrections,  difference  in  arc  and 

sine,  tableof 269 

M,   logarithm    of,    for   use   in  computing 

spherical  excess 271 

Mean  time  into  sidereal  time,  table  for  con- 
version of 113 

Meridian,  method  of  fixing 14-15 

Metals,  linear  expansion  of 315 

Meters,  logarithms  of,  and  miles,  table  for 

intercon version  of 301-313 

Meters  to  feet,  table  for  conversion  of 268 

Metric  into  United  States  measures,  table 

for  converting 299 


Page. 

Micrometer  alidades,  determination  of  con- 
stant and  value  of  division 12-13 

Mile,  decimals  of,  into  feet,  table  for  con- 
version of 115 

Miles  and  logarithms  of  meters,  table  for 

intercon  version  of 301-313 

Number,  fractional  change  in,  correspond- 
ing to  a  change  in  its  logarithm.      126 
Numbers,     natural,     five-place    logarithm 

tableof , 126-147 

Physical  constants 315 

Polaris,  apparent  altitude  and  azimuth  of, 

at  different  hour  angles 26-34 

aspects  of,  figure  showing 14 

azimuths  of,  at  any  hour  angle,  explana- 
tion of  table 22-25 

at  any  hour  angle,  table  of 20-21 

at  elongation,  tableof 19 

culminations  of,  examples  for  comput- 
ing times  of 18 

culminations  and  elongations  of,  table 

of  times 16 

hour  angle  of,  definition 14 

Projection  of  maps  of  large  areas,  table  of. .  37-48 
Projection  of  maps,  scale  1:12,000,  table  of 

coordinates 86-94 

scale  1:48,000,  table  of  coordinates 77-85 

scale  1:62,500,  table  of  coordinates 71-76 

scale  1:63,360,  table  of  coordinates 59-70 

scale  1:125,000,  tableof  coordinates 49-58 

tables  for,  examples  of  use  of 35-36 

Projection,  polyconic,  construction  of,  figure 

showing 35 

Quadrilaterals  10*  extent   in  latitude  and 

longitude,  areas  of 106-110 

.15'  extent  in  latitude  and  longitude, 

areas  of %  100-105 

30'  extent   in  latitude  and  longitude, 

areas  of 97-99 

1°    extent   in   latitude   and   longitude, 

areas  of 95-90 

Reduction  to  center,  example  of 7 

figure  and  formula  for 6 

graphic,  explanation  of 8 

Refraction,  mean,  table  of 272 

Sidereal  time  into  mean  time,  table  for  con- 
version of 114 

Spherical  excess,  approximate,  method  of 

obtaining 8, 272 

Spherical  excess,  log.  m.  for  use  in  comput- 
ing       271 

Stadia  readings,  horizontal  distances  and 

elevations,  table  of 290-298 

Statute  miles  to  kilometers,  table  for  con- 
version of 2P8 

317 


318 


INDEX. 


Page. 

Three-point  problem,  computation  of 10 

graphic  solution  of 11 

Time  to  arc,  table  for  conversion  of 112 

Time,  local,  method  of  obtaining 23 

Time,  mean,  table  for  conversion  of,  into 

sidereal,  and  vice  versa 113-114 

Triangles,   solution  of,  two  sides  and  in- 
cluded angle  given 8 


Page. 

Triangles,  right-angled,  rules  for  solution  of.  5 
United  States  measures  to  metric,  table  for 

conversion  of,  and  vice  versa.  299-300 
Wheel  revolutions  to  hundredths  of  a  mile, 

table  for  conversion  of 116-125 


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